Théorie spectrale en géométrie relative
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Title 
Théorie spectrale en géométrie relative

Title of Series  
Part Number 
28

Number of Parts 
28

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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. 
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Publisher 

Release Date 
2015

Language 
English

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Subject Area  
Abstract 
Théorie spectrale en géométrie relative (travail en commun avec Mathieu Anel) La catégorie des schémas relatifs au dessus d'une catégorie monoïdale symétrique a été définie par B. Toën et M. Vaquié comme sous catégorie d'une catégorie de faisceaux, ce qui correspond à la version "foncteur des points" en géométrie algébrique. Dans ce travail nous présentons la version "espace structurée" qui permet de comprendre les constructions classiques de la géométrie algébrique.

00:00
Multiplication sign
Commutator
1 (number)
Mass
Surgery
Discrete element method
Event horizon
Leak
Category of being
Frequency
Computer animation
Natural number
Topostheorie
Order (biology)
Normal (geometry)
Object (grammar)
Extension (kinesiology)
Arithmetic progression
Spacetime
Distortion (mathematics)
07:01
Finitismus
Validity (statistics)
Haar measure
Generating set of a group
Transformation (genetics)
Logarithm
Multiplication sign
Real number
1 (number)
Staff (military)
Proper map
Subset
Orbit
Prime ideal
Category of being
Isomorphieklasse
Lecture/Conference
Natural number
Network topology
Modulform
Selectivity (electronic)
Object (grammar)
Musical ensemble
Social class
13:46
Polar coordinate system
Group action
Presentation of a group
Divisor
Multiplication sign
Maxima and minima
Canonical ensemble
Mereology
Graph coloring
Sign (mathematics)
Lecture/Conference
Natural number
Diagram
Condition number
Moment (mathematics)
Physical law
Staff (military)
Mortality rate
Binary file
Complete metric space
Category of being
Curvature
Ring (mathematics)
Oval
Object (grammar)
Cycle (graph theory)
Table (information)
Family
Curve fitting
Directed graph
Gradient descent
24:29
Presentation of a group
Logarithm
Projective plane
Sheaf (mathematics)
Maxima and minima
Staff (military)
Grothendieck topology
Category of being
Curvature
Ring (mathematics)
Lecture/Conference
Operator (mathematics)
Network topology
Modulform
Object (grammar)
Metric system
Family
Spacetime
Condition number
Maß <Mathematik>
31:24
Geometry
Randomization
Group action
Multiplication sign
Maxima and minima
Open set
Solid geometry
Event horizon
Junction (traffic)
Product (business)
Subset
Frequency
Mathematics
Coefficient of determination
Goodness of fit
Roundness (object)
Lecture/Conference
Gamma function
Immersion (album)
Algebra
Condition number
Module (mathematics)
Focus (optics)
Multiplication
Theory of relativity
Topologischer Raum
Algebraic structure
Residual (numerical analysis)
Category of being
Arithmetic mean
Network topology
Summierbarkeit
Object (grammar)
Game theory
Family
Local ring
Resultant
Maß <Mathematik>
Spacetime
44:50
Point (geometry)
Divisor
State of matter
Logarithm
Maxima and minima
Propositional formula
Rule of inference
Explosion
Frequency
Thermodynamisches System
Manysorted logic
Lecture/Conference
Modulform
Newton's law of universal gravitation
Coalition
Closed set
Projective plane
Moment (mathematics)
Commutator
Ext functor
Category of being
Network topology
Universe (mathematics)
Object (grammar)
Local ring
Directed graph
51:53
Group action
Presentation of a group
Divisor
State of matter
Decision theory
Multiplication sign
Archaeological field survey
Sheaf (mathematics)
Maxima and minima
Mereology
Element (mathematics)
Morphismus
Goodness of fit
Lecture/Conference
Modulform
Energy level
Position operator
Condition number
Euklidischer Raum
Physical system
Area
Dependent and independent variables
Topologischer Raum
Forcing (mathematics)
Commutator
Equivalence relation
Carry (arithmetic)
Category of being
Ring (mathematics)
Universe (mathematics)
Object (grammar)
Family
Local ring
Spectrum (functional analysis)
Spacetime
Maß <Mathematik>
00:03
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00:15
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07:03
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13:47
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22:48
on the table at the moment the City of Light last year with you and the law In the the policy I'm aware that a lot they are also more fit in Greenland 3 yes it will but in principle and the last nation is we say that you is that there is key opens nationally by the whined to thank and now if I go Delaware not is there categories soandso category sorry "quotation mark aid after Michael Gloshen if I have a which is an objective in 1 I really did not like any the objective is that going this is a so if I have a lot
24:30
which correspond 2 mules I said in the same way that please flat please you he's not at ease if you will please Davies of finite presentations if you please of buying a presentation so in that case it
25:03
it's not the use or definition of finite presentation in Zacata category off it should also be involved in the form of a local yeah this is again because I don't want to use Spec so I use a B and a this is a disease operation all I don't want to use bad because they will use speculators maybe Nikos it I define space associated to the and fall and leaders I recently opened nascent peace you please and there In is a case of community rings miracle the definition of the definition is a property of the recently opened national but in fact is a restored mentioned in category both the fighting schemes to news refined scheme are exactly the flat when more finally presentations and still I say that's funny now uh you II was included the community please in ours so face were flattened physical by so the for MEI FIU flat and there during the some finite and said said from the 1st day and nite such that this is the family deal from WI Clipper staff from the mainland to the Ironwood these consortium this is a felt that condition and the 2nd definition of family for the dice legal for any I can't fight is there various key opening and for the 2nd 1 is this so lysozyme in reserved I do you before this tool definition defined the Pelosi and so we have defined on category past this is a fistful for of practice going back and do that is capable of doing and we know that Zafar face for reflected incompatible he he said can only go so that is key that is the 1 sold so we have to sheaf of this guy for the FF to sit GE which is included in the should for that is the topology and appreciated his last hours over this is the the of this down are not smaller but you can define a apology along with the don't let me know if you want to know what I would do just now I restate the F. that's all way 1 minute and then we have this there are unit I'm not I we they put this offer of 30 presentday borders on sea and in fact they will use the following day I thought it is because we needed played up in I don't intersect but insist that they will need later that in fact 1 is generated by someone the multinational finite presentation In fact we can see that the end of this category if I defined I played with clear as the opposite category of the category of wearied of playing a presentation I had in the same way which is controlled project in pain in and this 1 hour more categories I will be needed later opt for the moment and that they don't need that OK and the more I would but if you want we will you can do just now was site but is this so we will we for dentist apology because in fact for what we do we don't need this topology we will use all users that is capable of doing analysts said we want to defines this new word Joe metric object buys a phone bills cancel the we want to say that
31:27
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37:48
set with 1 imminent and in that case we take geometry so I will vote this is 1 definition if 1 there is another 1 to try and before the date set appointed this is the 1 that I have this was much in that this week because he knows this is the 1 that I learned to use faces of soul in Ozil definition of if 1 In much the event of a ship that off and there is and was maybe 1 way that I am not the fisheries that 1 way to to sink about hope to die geometry but it is a EU is to pursue their for the category C the category of 108 people for and would you also In the skeptical you consider an algebra II recorded so this is urging railways with projected With the use of your predecessor this is the 1st of his 2 3 and a lot of work that has some Florian you of what went persuaded where is this is this 1 focus and you can defines the word to geometry overall the although beach you considers category of the modular proxies category of the modules and you can define new geometry which is freighted with topical but I don't know exactly we need to speak with people who make because between 2 what is exactly the relation between these 2 tools since the that's what we will have a summer change of context and the threesome you can do Princess Atta skin is definable as they and EU you can see this came as a key indefinable role for instance and so on but I don't have time to think about that and we prefer to speak about the Mall Road recent result which is a bit from so as I do the following the day on which he's machines and reconsider observe the deposit all of the was key opening immersion although i've this is in fact for the season the Post and in fact the teaser afraid the thing that you have a good thing but the frame so to Caesar this tributaries lefties complete distributed last and there this a so the other category of French zeal for that category of free a category of gone and so we can consider this insists category so we consider this as an object in category of broken and we know that there is a junction so this is the right John .period and you know that don't open subsets from the category of the political space and now we conceded the maker of the still can't not mind the photo of .period for this unit would be costly and this is what I recall suspect this spectral so well defined from top Spain From the the category of sheets to the category of in fact this assault multiple political Spacey's because we know that the major is formed .period our the so little spaces that's an asset a category of .period dogs replied that over and this winter good news we scored needs and he sends a zealous killed national stole bullpen International laughter political space so what we have done we have associated to which she but the political space and this is that is ideal for the visit what is the 1st made the definition of a scheme to befell the condition of the game is a topological spaces with solid structure authority and believe that we can actually we have tried to do the same in in this context and so we want not to define a while at the Xanana was also burdened look at hearing that space so we what we want to define the what the plays a role all of the shaved in local ring so you lift on your values his what with his cheerful about the case of the say at the beginning that I will use only this apology so I was looking to problems over the world the government should direct the high violence the and that is just you and know this is the way meaning that only those who who value the most visible about the
44:51
Menendez observations allowed and then you will use the Yugo the yield on the environment and it's sort of reserve soldiers who who have you been this close to realize that there are yes or ii fall that's that I need to do to users after In this spot now I reuse 1 OK this is the reason why I make that the decide what is before "quotation mark the word I would like to here meanwhile need Bush since I if I take appreciates allow yes I identified I am not sure that I have a fear of government is couldn't but for the moment I think that they don't need the news wasn't but they will use it of shapes suggests that I don't need it even so maybe 2 just a wee recourse seeing the Bowater foods is a reminder of about 2 posts just if a date the fire for me wasn't always the "quotation mark and the and so is a category of Joe metric more front of the but was offset 3 to the which is going to the category of point of view and this is a state of the pair of a joined from toll fraud he was a category said With these includes the left exact the kind of already sees that and that if any this a category of appreciates owners more Category C then invited .period all the is the same as a category left exact from duplicity is smart category With cyanide 1988 from To set and invited to the saying that category frosty coalition which is about to receive In view of the good people who used to be the opposite of the things that I want to do is just a small portion of people not only because of you 1 of the poorest of the poor this year or a year existing again made it through the reason why some people according with barely enough to you want to use the convention in August so that this rule see it's not least is the opposite of the universe way we yes the so for me it's not too early just to say that in that case In the case where he is the category of seats for some topology and the topology told is defined by a quick Apollo DN is defined by covering friendly we as a point of you in that case is a form which shares sank I said I don't write which sent recovering from Wiki Moffett funny and what is important is what they get that is what they recorded a lot the and they will interview where to obtain I'm sorry because I can't stand so so thought I say that an object if its interests in Israel ,comma leave for any while being the for any faltering familiar and for any amount from its 2 the increase a factorization might solve some object on the covering from this is what I call objects only the of the week article in New World in Newfoundland history both because it was 1 of its strong fickle was adamant that the data was vilified Multan is Iowa and there always an the issue seemed in the category of commuters hearings which will gain is exactly the local rings and with people of liturgy but it's not important for the moment and so we decided not to which is at top policy of sheets for those out of topology which is the source of the reports of 1 which is that category for creation and we see that the point of this because Our so is with a cordial .period object of office which is a subcategory of the bombing 1 of the categories appreciates which is a project for objects of art and by solution is exactly Q and now we have 0 2 propositions in this proposition is quite correspond to was the she's
51:54
all look any renewed spaces for anymore it's in the category of sheep there exists the Sumatran coffee so I could always recognizing from it's
52:24
a category of sheets overall stake in tools and I will give you some explanation may be In the case of the commuter during this element is in fact designer's that is and this is the specter its use topological space as a I have defined the form which is associated to my skin so I have a political space and I have this not and this is exactly what we do when we have when we consider hazard is the or eats know the usual Austin it is exactly this because a lot what's name to define that exists genetic Mofaz In fact to define weeks he is equivalent in fact to the following who 1st is equivalent to 11 not from Zary defined the kings of finite presentation to 0 category of shapes the recordsetting but this is a census to cover the only of the cities of desirous keep although it's so which is the next exotic and sand so covering families To win of the more families tops and this is a strange that 2 of the photo from after prose that it's all To and said the category of said 1 which sent a letter to you To this end of all known what is more chiefs from you to so early enough time to convince you that this is exactly what we but is a sheaf of colleagues in the usual on context of of schemes but this is exactly the same so I wouldn't be enough time to seasons seeing about factorization suspended but you see that when you concede there more fees most schemes of usual or ski and you know that you observe the notion of local animal feeds you cannot concede or morphism between even look at rings in wings of the notion of broken off inside I don't have find tools to explain this In states yes all but in fact and this is you have to define it as a liberal offerings and we can define the same notion awful carrying of rollcall morphemes nods and delivered all of the 108 then we can extend it to obtains an notion all local morphism between a rock and hearing that on the 1 she and this is what we need to to obtain Zulus to last 2 reserved maybe so we redefined as a category anymore and so this is a category of proposed to raise the map toward from 2 in London this is what we call a structured the so we will obtain 1 and in this category we are not the subcategories which is not a fool said with the same objects but ways to local markets this is what we need and in that case this is this is the may maybe the the more difficult part is this 1 and then so this category we this people and more proposed and according to law and if I restricted now attend restricting in fact to wounded look at it boss so I can defined area of story so long because of the proposed uses 10 season has the full force of all in the space and in the same way and 1 of the following and so serenity the following so we have a more From the category of sheets told this category this is this Morpheus is in which it we found effort 2 suspected we've always suspect as is most of those space and all whether is says systematic from spec Esplain won with a time of the final before for this airing advantages of which is continuous on this sounds artist opening national panache and sit there are but but it is important it induced an equivalent of that Italy between so that the goalie both schemes identifying before and this this is a category called until next week schemes and redefine what is rumored to be cleaned and human experience it is and objects in this category which Israel caddy for the usual topology Liu whether it is a cooperative space which locally a science geek this season look at it defense and we recall not exactly is equivalents we have between the 2 definition of schemes of fall of our community rings In this definition is a definition of yard in the gym the political scored space between locally the Wizard look at hearing the states which is locally find as is the definition of skin I did at the beginning which is the definition of skiing has formed off looking there was no responded that the decision of the president of the American Institute of the responses to the survey I have the distinction of Americans and they suggested that the work of the residents here more about groups of people who are very special what this this kind of work where was the verification mission next year the categories of I think it will be so that gratification he had and that he values the levels of the questions you get the kind of political yes know this is yesterday and if you want to duly news that in fact the system someone with wisdom that you have to to stabilize and in fact you have to use something which is like spectrum and Eureko Wilson's unless you you you can as a yes and you can define whom Wikipedia To security unit in violation of the someone Georgia the they do have to pass along the good universities colleges and high quality of the images from the history of the whole here about violence task of this time for incentive if we want to know that is capable of you but it died apology and I think this is the way to define the type positions that you need to know the Boston took a year and a half of which is the goal of this show so why was related to the fact that this solution now he and the security and to apply to the conditions in the Of course the support of the U.S. should make sense contact more what