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Motivic homotopy type of a log scheme
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Title  Motivic homotopy type of a log scheme 
Title of Series  A conference in honor of Arthur Ogus on the occasion of his 70th birthday 
Part Number  11 
Number of Parts  12 
Author 
Vologodsky, Vadim

Contributors 
Abbes, A. (Organizer)

License 
CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/20245 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2015 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  Given a log scheme X over the field of complex numbers Kato and Nakayama associated with X a topological space X . I will show that the homotopy type of X is motivic in the sense of Morel and Voevodsky. The talk is based on a work in progress with Nick Howell. 
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00:02
and so hot show me the end of the day and the Americans endure very much for inviting me to speak here it's a great pleasure well idea and we have become berated his profit on 1 long project thinking for wrote the Yaris and this was taking the most fruitful time for me in mathematics and medicine to that I I learned from my what their books the news and what it would be to have knowledge of folks scheme and the fact that in this this this is the war crime going to talk about is there for while we are also from question that we discussed whether gold is on the phone so the question is fully so I ahead for most users and then I had varies from 0 to you as well for example in the later part of the motion all war saying state and so if my most scheme happens to be defined overflying fields so then so this is like I had decided homology of Xmas curious coefficients well it said so that the space which is equipped with an optional there from being used and 1 can call maritime rights and 1 can show that for the reasonable are asking let's bearhug innovative the numbers of course them differently but in particular because they're the numbers this gives me the filtration and so there there the question this sort of see with we use is still so can 1 guy defined consideration dramatic well so I'm going to have a definition which would make sense folders the furious In the end I will harm more precise well so you can then ask for rational beta ,comma joint can ask even whether it's it's defined integrity as for usual singular from knowledge of how to break rights and so water will also run can ask whether it can plan associate with it was the motive for the 0 per cent the war media 11 a final question might still come out of .period please what I want to tell you show a little bit about this question so what kind of homework to be tight you expect of him so sold this vents were so lies in their construction due to Crichton a young man so became so I wouldn't call it here at the end of the month construction so they defined in Beijing knowledge Arkansas Hurwitz perfectly so that's and Richard which overlooks the Mets sleazy coefficients and coefficients our will to be by definition the military officers and the biological space so this is just usual the well so this is a textbook so that's what on the explained to so this is adjusted the biological space well in many cases it said woods yes yes sorry this you might might exist power over all the public thanks thank you so exercise will skip over the complex numbers and so this is the start of the sex the bro it's it's just contributed most biological basis but while in many cases it's too many from this boundary passenger from structure so what is it still so this is the biological space which is equipped with mn it's proper all of yeah and to them and so on will also the conception is that the fallen so are willing to have my books scheme so I do hold by its underlined scheme and enemies is that sheaf of monoliths 1 still well so I have the sheaf of my knowledge they have what started that season cited and they have a map the war so well the only the nite here involved it's in part of this well that's true for the call for the entire article is good completion and groups so this is a a sheaf of lobbying groups it has was stunned season and that has cautioned we cherish well ,comma playlists you have a look at the fine look schemes so it's going to be a contemptible she why 4 are both for a time the bulletin or if you wish you can consider version of it for the despicable Beauchamp fucking Michael it's you be more convenient to consider all the says sheets was a stupid apology are because in the end from the to the well itself so that that's are let's stick to the is so this is the a big think of this as well good examples of such land that is just the quantity she supported right still passage in existed and are OK so to a scheme and such an extension I want associated the biological space Soha want to do this well if I have a Boyd well I can certify received my so that is here information man .period events and so from this from this extension I can derive an extension "quotation mark there stallholders chief lender boy index and this will be a hand White state 0 this is just there finally UK generated Indian girl and this the system on Stewart's extension Monday so now and then there those who saw yet doesn't mean the Stockett means bold Bush out so in the here I have from see started this 1 which is called so where would this evening to this match its code ,comma so they look at all possible sections like it's real policy next so satisfying the property that's if I compose Gamal this Sigma I get out and so I think sold here this is the thing that has was being in our world Bush out of this section I still and then this this space said said is just set of all players in handling all along that we have to use do this or is it Nunavut tuition fee I do I'm going to assume the 2nd I do assume that it's our offense but for the moment I don't even need this so arcade have room so I consider all such legions of course that is a and they want those so their fighters tell me about it Friday over the index is a practical steps forward forms from London said Dole S 1 so In are in the case of looks the manifesto scheme suggests that video stores In date and so then that is the bulletin 1 story in section of Group the fines that assumption but when it's Walk His videos in Aswan namely it takes buoyant X CDROM signal effects .period enabling these functions would be continued so I consider politicians that they Bobek of anything use functions and excess continues as this functions but so and that's that's the political space and I want to the idea I want to see whether while I want to on the ultimate goal could be it would be a dual realize this the commodity died world leaders at home under the title of this book space Center Machida Vermont epic so will there so the stability of such construction was such that the might to me by oldtimer a goal by our moxie and also by my from proindependence from the same time so they they explained the new 1 single example which adjusting the defeated a key example so I want to I want to tell you about this example is of this said team OK so what is that so this medicine looks structure that looks space on the it comes from hazardous do this most especial find office in stable the DOH so it'll do this visited the exhibit Dubinsky and not so since stable the JNA so it's mystique and moreover so I will assume that it's it's there there no are like people intersections where NEC so are there might be Chernobyl nuclear devices that will be conveyed to you know it's a case of many so I have this divisive and 1 gold you and are sold and the name have who outlined 1 both fun and 0 namely have failed to provide beaches speeches from all of the CIA restated that here so far so this is so have I don't want black people and so this daylight comes the stabilization the fight restated his another piece of should you II is withholding its 0 minus the Oxo underlies the start when this dictatorial eyes contaminated thank no so far this listless structures this this or that line bundles together with such stabilization denies is given such 1 bundle says the same thing as that given an extension of the z z because it is the physical the violist and this is this is everything over and 0 so Our so I have 1 1 and 0 I considered serious scheme well they look structures just fall back on structure and everything given by the my said so but will this embarrasses has the spot where a simple description so these are the constant shifts under 0 1 GI expanded to them Everything from so on and they want to but in this case I want to look at school and the allies in the same alignment of the anyone who wanted the cat think so well what should go on I so where is the fall in so I will leave another piece of medication so let's call silk this will be a GM post associated don't talk the only Aliza line bundle I think that those places the movie's usage in the town so and then so what I want to do I want to consider the following complex now the full England itself starts out so that when the concept a well was demoted and well in fact that he'll be even element stable homotopy gate and stable after 7 modifications so long OK so what is what is this has served as the discovery defined this amount so well I want to do something very very simple and it take on show also gained the society is regarded as a scheme but leaving all this year and they went the restated goal you want to we are very soon sincerity I think 163 at all costs because still when you and then this is the 2nd in that I want to do I want to take over tool interesting they want and so when I write square brackets it means that I consider this a somewhat just it's plain schemes so how and what they'll have here is you still 1 time spent on over 2 0 restated 21 OK so and this C 1 interception great so well so my mind motive is going to be 1st of bear the quantum of this man this month are know or are you to tell you what what several so and there is a reminder of sold well this this construction is possible because well in the case aggressively was too modest to have identification vantage of the variable "quotation mark of most many voters this bunch normal far mainly a few half hour are or so smooth y and z this this was a smooth then there is a canonical man From there most of the puncture normal bundled I don't know my wife the point is cities and differential geometry this can believe much of it and will demand that they have here is exactly will comes from but this is decided that meant so here is a picture so if I have that's the secret of the University of silver and case so here is my sarkozy 1 for example and here I have this 1 bottle of reaches but beaches I want to thank so and here I have this is you want so .period is construction stories have recovered this this this line bundle this year costs of the peace over the hold you want all and in this inside this the total space of 1 I have are of 1 mind as they have this this fight there already want to direct flight is construction Gold why this this is GM's 1st of all over T1 and Zedian it's fine that already want many precisely this 1st met on the secondments constructed so you do this and do that Bloomberg said to whole of didn't think that it is in sense here that must be seen at this 1 In Fallujah several things that the these other than those in the normal manner in Indiana well so so I don't think that there's any sign this picture so maybe it seems to me that it seems to me that that is here than its incitement by well I sports so are looking so far in fact this this meant that they used here is a semen In In anyone from what just an 81 home a dedicated but only after suspension show are so you can you can kind of the same Our said that what you will get you cannot get comic book the title of its slogan so but you can't get home at the time of the suspension of so if you still get something in the stable ,comma so defended this that map exists on the suspension of by Martin doing so Knock it so and will 1 1 more remark about this this this whole picture and so are enveloped this this year life have additional structure is may come from the same stable duration mainly in London Desiree not always is the evil well I I think he's began this realization depends on the choice of a parameter here will choose a T Gordon right because this is sold you run was so deep provided leases from the bits of and therefore well if I might have a man from from this from everything in this this and this and this picture I told you so 0 pool complex numbers right so so there is always the met from laughter from his guys the complex numbers from 1 notable context right show are and therefore so there's there's meaning this this call it art motive look all get 0 so supportive of the folks scheme condition and in fact in this case this this much if it is not it is much safe I want to Over the system and its fibers for example while you can bake fiber so absorbed in every area of scheme here is that this is a steam already status so you can bake fibers you have do this met it gets what's called their most 9 so and there a bit teachers serious I cannot see you draw a picture of his viewing of the 6 flock but this it's walk he argued that actually it's it's for it maps stole from my outlook space associated local boys so it may have to this article and they can go at each of the 5 all these somewhere over Over the point of this article selves imagine that for example you have the generation of we need to cover show OK so here is my soul the gene rational surface tho that with blends Nike that's so insists announcing the insecure and this now it degenerate so what you with you don't of the Fremont this book points and then he'll go along with the budget to be and then you get something back while I'm out of the current intelligence and conquer and so on so I want to kind of extend this construction tool "quotation mark skins and that even if you have this seems stable case if you have mania components and multiple perception becomes Elia will direct this year G resistance really unpleasant because well you can you can kind of fried down then the senior Congress but well you have to do is lifted in some level and then on the square of the differential will not be 0 Hildago home that they couldn't 0 and commodities are given by some of the 4 that normal Kwan constructions and so it's it's going to be completely useless no possible you can't really do anything so instead of 1 should look at their Dothan man should look at the to promote all all this of this mode and this has a very simple John metric description of I'll show it to you today and in the case of our this seems the evil the generation but 1st they want to formerly the main feel I'm the kind of the next platform for the soul the rent this fall in so willingly did beat and the US introduce a bit of a civil Kittery the new code the caterer locomotives but where we then too you can use it while they can forget about the stuff I mean South introduced a category that the local ticket afloat so and in order to do this so that's why let me just right down the definition of usual category of what the motives and then annually still more you can defer relations and and you begin to get off the problem with so will still idled work this out of the sole apartment is so ideal assume for simplicity that's characteristic of my away is is his hero Williford sp you can you can do the same thing but you have to be the coefficients and then found looms so the OK so fully with the motives for you do the fall and the much of it so your you consider it it was the crazy video of last year's sale find died over over a field and then manual formed agent of critically I just wanted to say that seems schemes finding type and morphisms value combination of of minutes no Crispin's can be and and then I want to take the accomplices finally there is this and then I take about 5 more developed by 2nd Edition by Sept so this is a wily fuel fuel you can do it and think related fell by spoken with that the conservative and they couldn't get portable you can you can regarded this a differential with at so and what I wanted itself so old will try the so will ideally use them that's a litany of specifically here are optional ,comma physical took is "quotation mark this winter because of folks right so it's ex parte so soldiers Sara Colm this is so full of schemes right so and so this is fewest Texas quality went on with the game the move and then some but the 2nd class of objects is that will touch have to that means that in the here so this still still this is the 2nd class of objects are notified for the disengage the apology so this edgy rates kind of sequences of governors and so there will be a box well that a suppose I'd have all but they still open up and they have an indictment of the this is followed and so what are their conditions condition is that In the man being there self from the export of minus sealed the deal Dole the X minus field this meant the distinction is a measure of stops so that means that this is diamond and on the compliment to you it supposes section and section why so on this is all there is still and this is a bad isn't particularly you and will ,comma fixed with as much much much more than and in the end this is listen I want Croatian and assimilation has informed its you and I will use and here I have decided for you there you so both and so this is part of the and Bobby and so I want the fallen anyone to reconsider the maps of the from exprime Linux this separate and I assumed that the disease that causes such scheme here this is the mission scheme says that over the compliment Is this is their rights and so are the produces an isomorphism between the army the India's of its minus the z and its mines His for example so OK and in this situation I want to have the following deletion that for much of Wall script Surprise lost the motive force for a of overseas that meant that this this Mappsville motive fits him here at the world most of the show of of you want to say that this year I have to post signs so either of those incidents earlier this in year so I have to take the set the races could still I can't really see the school's the and also maybe she knew on the she is the demand from yes must nice the Nets in the postSoviet because there is way that pocket on the basis of a hearing so many things that follow from from others oaks and a well you you can you can be sold so this is not too and it's not there so can Her are so this is not what's what's called usually called the was was it's also defiant and studied by every was key and it has a very complicated innovation on this case the the school fund so let me the real hero still it's In the long run and then this year I think this is the whole schemes I can't think of income from Monte so what is there to deletion of this the skating career is akin to that of apparently was scheme which is so that is a world that is it is a defunct so the disease I hope we will stick category which obtained exactly in the same way it said that you ate transcripts so you use that is our noses consider the same relations but this category's used his is different you into schemes and where maps are finally correspondence not only was something that if you do our oppose it makes it makes any difference I don't think so voluntary groups to new you also invented the smallest games than CDs the Bojan than me is that user can be derived from for me and the other funding so now I want want someone lose motives Howery ourselves on just consider the same same involved a similar pedigree but let's that business is all about so I sold by my little schemes so considered I mean if it's kind of a century Paulson said case and then I want to take a so I want to consider the quotient of disease well look he and brought by federal cheap will enjoy this so what this would do this to walk well it's so hard to walk consists of it said .period president a lot of our or injects well In joke also died 1 full and careful so I need a little Temple is indeed more than a few more relations so while the so what this would do this the relations and so will just before we and displaying the relations also what I have here on this of of that is ,comma the vehicle installations so in this some of that because relations it's is allowed to be looks cute as well as here so I want everything In this feature it's well this my new for everyone they want you usually but I don't have the ideal and axiom formal there and it's because of those of his 1 of the longest show of the so what what I want to use as a falling it's him so I can't he want look so what is it said it's our and underlines the Musee 1 and built structures given my 140 so they might be Andrew Lopez just as corresponds to the line bundle of this point so and here I have and so low look for and it's kind of their origins and considering GM has the structure so and Ireland this maps to be isomorphism my quotient creative but not the only reason I want to modify his wife Maria but it was for and they gained exercising his talks show and also this to the consensus is that it the well there is 1 In addition stations it's a just passed the bill there in observed that will all the construction we have made so far depend on the on and groups not an end in Missouri and I would consider the category of hostages with the category of extensions the what is it with them I'm in my category tea so you won't be here at all the fear is that a lot of reasons for people you only this this year so this whole differently for example is this and so on In and finally forays is really ready at strange well so it's it's already rented his opponents of so suppose accompaniment be from exprime it's the schemes and I'll be there they underlined the need to use usual schemes is Nizam In suppose that it induces demanding users of want and groped her fear of a stock write to them rental this is a nice then than I wanted to follow in relation that best price because this month so this kind of a way to say that everything depends on them for the game so I could become consider just the Canton of affairs explores this extension .period this must show on now our voting with some hidden during the winter of lessees who plays the role of a row over the years this phase of the moon of space local governments companies while you can the soul but his appearance so well they have category England CCH this is my catering here is the name for this so this is not a 0 sum games Hoskins so is of course a founder of this larger well would I think that anyone engaged in furious serves you right we welcome for him he so right so this fund is an occurrence of created so what does it mean so what are for example found that from this category who say the conservative ,comma the aha disputed strike that satisfied is with the property of the state of the claim is that the whole motive here is going to be extended uniquely Goldstein's provided has orders OK so long as you so let's see what so and particularly well of course qureia have the governmental the usually was the case in and no and then them composing verse and get their instinct now so that the construction of the pool is as medical uses very little Johnny instructed it's moral as being about to run and so well festival in all you have to prove so the excuse so you have to prove those things that are this is something that they have here is the oldest of the that's given into this swamp that is called it's fully free on whether the gleefully faithful it's difficult to think of this as you still think don't hand indeed so essential subject well and it's not so easy it uses step with that the implies implies B and therefore prove so so all you have to do is to prevail so and that's because and the UPN goodbye induction dimensions but not so you have to show that the union what if offering the lock scheme used in the middle of this although this fund and so have enough relations that express a motive offering you steam in terms of motives or from of over that's that's easy so you the game by dimension of your skills or if it's 0 dimensional them well it's it's defined as saturated so it means that my knowledge group is just that as you do then and a so France so so little the correspondent so if I have a buoyant and they could well it's motive for example is motive of GM and different considered Cartesian product of offering of any scheme of work .period is itself and so the 1st of the G Benji and followers from from from this and so any confusion using this property anyone 0 dimensional scheme as a senior differences but it's productive so now about what you're doing onedimensional case so you have some tourists are well armed now Our GDP or whatever when open said little structure is obviously the really just as good responsible to the expansion and groupies is is just the extension of the and by and my virus stock in the and therefore are OK so you know what to do well on allbutcertain than yield you can use this answered Egypt's soon tho all this that this this what much of of the secure offices also so what what it is is this no I used because the because huh will if you look at this each CGA ships you always looks like so you have some are the interests of disease and then you have strong the plots of exprime this to prior so what's so I went to a show that then this I just started so that the soldier as the soso knowing that the soldiers and the sort of tying the image and also they say when the construction of a conclude that the subject is ending but then I need demand from Annex From this polemic attest to this right and they need to show that this man is used the usual category of we Will you look at the way was to consider the disease by diffusion of service because that's the exact triangle that is a man from square bracket then still does not please the shift my wife they need to shoulder this matter actually exist show now so what you do for the good of the whole thing is that it is I use it it's very still operating so I could get close to that of all the colors of the 9 Eagle workers about the poetry rather than Missouri schemes and the world and then they'll get in and out of list of wealth application that I had in mind have to do is seen to grow the completion agencies on the polarization of usually with incentives and so on "quotation mark talk I mean so watch it all for our 40 so so what he has still not it's enough justified by a former nonsense and it's enough this to prove the theorem it's enough to build on the fall in the so given menial jobs are also all of this of this category 1 of each of usual we want to see each on maybe you just say the following sort it means because my time is short so I claim that it's enough power it suffices I will serve the surprise there completely formal but also from the uses the fact that the category of was due motives is allegiance nor its suffices for our goal shoulder that's far from the defunct call right this is your friend thrown forward this the usual category of Johnson City each of the them 2 can current expense 2 right "quotation mark larger which this this is right representation that is the problem and I want you to hear are so you'll hear just such a fuel you untangle the defined Mitsuko that knowledge it's not quite finds it's it's calling this the skating there is no transfer so it's I don't want to school expenses ,comma good images motive consider this skit stance so you want to do it for for a new books and ideas very simple your are sold on world you have the the period can be eliminated it can be considered at the summit achieve 1st of all this message to the part of the Government and the Alliance chief or that means simply that he believes he or any scheme which is small of war Over and over this he simply bulldoze stature if I have a man like this then again Bloomberg stature whistlestop journey here and there there this summer so far and then what you know you just can't shoot his age the current knowledge all 4 of our the effects of these coefficients and semantic pops the sign out of generations in the category of massive systematic part of what they defined by wayward students made characterized by the property that they could be Texas isn't that much of a ski mask is the semantic part of motif of a scheme bands the motive of the semantic borrow the of the world just so for example of what happens if you think of him and his wife who was full of you don't the lottery or what that was units of the new people of India and what you you're new so for example what is fierce well Montevallo duties it will want to suggest colleges hunger stand aside look of the Peacock so locate and now will I went to the news by those this is not this is generally of this so so well you will follow this is a little here this is the series sugar Moger all this material on this matter which so sold far well I want all the news by a very explicit formula that I promised at the beginning just very for them at the local knowledge of the minute motive in the case of since they were Jewish and also for the distributing it to albeit not just in the case of singers stable generation of comes from this by Justin worlds it's on this form always is here I just want to or I'll make explicit but none of which is which is 3 0 from visiting so the formalism fallen so here is my Satan will now I have on Indian and have there they walk structure of common from seems stable deterioration but now it can have on multiple intersections world but still seems stable maybe that's not a good pitches so this should be a place where the lines so far from the village of national for the here and now so I don't think use in the competition is stable the generation and that's the right so I want to be that's what I want to look structure for typical of state fatigue from sticking seems stable in a stable the generation so I have components view on the article the World Services subsidiary ii behind Alonso success right have this Jim Dawson stories have relied reaches 0 they stated that that Our and then I have the decreased when GM doses and they have reaches a point of view and so OK so now idled by producing the sense that the matter from so for the 1st time will produce that Holbrooke form of SMU's Florida's forums you the finalists will be a the moderator so what does this say about marriage so so the plant corn it with very simple .period of books most worried so this Sylvia of all this but light so this is a product of you know it's a it's a it's a tossup all on 0 to break the ice with dimensions who is now what is the next storm so you take this sounds 1 let's face it said was something want it's not really it's profits on defense at the end of a major victory I want to make sense of sound so it means that this is we wouldn't think of this a joint and so on the prudence of I didn't find ties not included and here I will have to follow up on the sale stock thank you you I told you so what is meant the member that analyze the yield or you are therefore such just you by swelled section now the incident logical next and here's its luster his son by there over hence the intersection G. not for the life of the G 2 and salt all use here although differentials come from this section remember that paralyzed the the evil all soso this has given such a game this distribution and so this is that what it's very simple ,comma it's now are formed as defined by complex said no 1 to 0 5 well what you do so you this is and then you take a where the following so if you have a scheme over it's 0 then world the lady off my home suspicious and 0 meanwhile the is a fallen you'd take correspondences border 0 but from what I talk this this complex so well informally you just exceptions all of this hundreds of rioters were right and then you make it ,comma be and my point is stinkin here so far let's go this this this and my Matsuda ,comma legend there also there are 2 0 down Missouri yeah His Kansas City's from origin of this experience with qualifications In sense that's all I have to say so there is 1 well that is as you see it it can ask whether there little geometry here and in thought that is there is no majority is the it's just the amount of Randall the fear is if you want brawl for example that if you have a small scheme than its most it's a isomorphic to the motif of the open part wellbuilt structures that this I don't know how to them I know how to do it in the case of like normal person international crisis situation by the Jano class engine thank you very much Will the application of the good formerly used a similar to the end yet so so here are a defined and there is 1 and its this and this is absolutely all this set of Anderson I so if you want it is defined for legend In this fall for larger and right you have stalled just yet you need is the whole construction stamp duty ways former who Bloomberg was smaller than that of the Union defined for small raised by conciliation it's advises the defined is full of institutionalized number has these flows whom he is not just might on all year so so if you will if you wanted for some of the you have cancelation was also you can express their magical a lot of strength in respect of quotations as your friend in terms of how knowledgeable of the parties this confusion since and possible to solutions "quotation mark this year's near the end product of his death yes this was the reason should have the right to hold the idea of this this and this was to be the hearing was and so 1 yeah it's that's that's very good question it's that this this this whole or conflicts of schemes these over Aegean you even if you have are few have this is exactly as in their speech I start at least this gives you the 2 variables "quotation mark are if you want if you want to harm you believe that they deliver their vacation cyclists you'll have to take the fight over the over all of them so it's a it's a Yeltsin the bottom magic she what overdue How do I year revealed to the the not that it is a rather than them after GM plants from the digitization of the tens of comparable to this 1 1 so so he she should this 1 this smooth skims over all of this schemes over at 0 admits some of the GM for example because there was a lot of things that the product is there the police have said during in the public the political position here this is a reasonable rules people are waiting years so there is some the Rothe a soso year sitcoms thinks the were combined so if there are major motion the IMO drove the mode of the need we was to much of is achieved is integral the Federation the show that the national you do what you has have here had reminded him with the news of the silver was well was here you don't have a lot fewer you don't have that we have to show is that there are no better than Whitaker modes of its locomotive that they did obviously was King would have redefined sites used this Moger of this device as defined by the cut in the Yemen but this is all just because of a cut in the Koyama motorcade theaters displays east of all absence and therefore on this front the from what motives is uniquely determined by its distinction tho you don't want to force the usual schemes that is an integral part in the 1st time he will and yet you have to be handed over there what you have is that there a sky in gained so that there won't be a reason why were presented here is that they want to wear was the must've really funny staged a portion supposed was the motives for the college losing our lives there is no clue is the result of years you knew you know I don't know now maybe that regular use of renewable fuels you thank you what
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Insertion loss
Complete metric space
Parameter (computer programming)
Mereology
Grothendieck topology
Mathematics
Manysorted logic
Line bundle
Homotopie
Daylight saving time
Square number
Cuboid
Extension (kinesiology)
Fiber (mathematics)
Position operator
Stability theory
Area
Process (computing)
Rational number
Sigmaalgebra
Nuclear space
Mass flow rate
Generating set of a group
Moment (mathematics)
Homologiegruppe
Thermal expansion
Price index
Variable (mathematics)
Functional (mathematics)
Measurement
Metric tensor
Isomorphism
Hausdorff dimension
Quantum
Normal (geometry)
Right angle
Resultant
Geometry
Flock (web browser)
Real number
Heat transfer
2 (number)
Power (physics)
Wellformed formula
Ideal (ethics)
Theorem
Subtraction
Field (mathematics)
Condition number
Motif (narrative)
Addition
Shift operator
Multiplication
PoissonKlammer
Forcing (mathematics)
Element (mathematics)
Projective plane
Incidence algebra
Axiom
Differential geometry
Voting
Combinatory logic
Fiber bundle
Object (grammar)
Coefficient
Matching (graph theory)
Local ring
Inductive reasoning