6/6 Perfectoid Spaces and the Weight-Monodromy Conjecture

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6/6 Perfectoid Spaces and the Weight-Monodromy Conjecture
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We will introduce the notion of perfectoid spaces. The theory can be seen as a kind of rigid geometry of infinite type, and the most important feature is that the theories over (deeply ramified extensions of) Q p and over F p((t)) are equivalent, generalizing to the relative situation a theorem of Fontaine-Wintenberger, and also implying a strong form of Faltings's almost purity theorem. This method of changing the characteristic is then applied to deduce many cases of the weight-monodromy conjecture.
Point (geometry) Addition Functional (mathematics) Group action Perfect group Multiplication sign Projective plane Characteristic polynomial Line (geometry) Graph coloring Equivalence relation Power (physics) Field extension Category of being Root Modulform Körper <Algebra> Algebra Resultant Spectrum (functional analysis) Curve fitting Spacetime
Classical physics Point (geometry) Multiplication sign Propositional formula Category of being Ring (mathematics) Logic Order (biology) Object (grammar) Boiling point Resultant Condition number Spacetime
Logic Closed set Limit (category theory) Physical system Spacetime
Residual (numerical analysis) Pulse (signal processing) Group action Ring (mathematics) Total S.A. Körper <Algebra> Limit (category theory) Condition number Physical system
Category of being Multiplication sign Physicalism Maxima and minima Limit (category theory) Fiber (mathematics) Spacetime Product (business)
Mathematics Perfect group Ring (mathematics) Link (knot theory) Diffuser (automotive) Netzplan Limit (category theory) Extension (kinesiology) Resultant
Goodness of fit Variety (linguistics) Moment <Mathematik> Right angle Condition number
Torus Point (geometry) Projektiver Raum Group action Term (mathematics) Modulform Right angle Open set Flow separation Subset
Causality Sigma-algebra Moment (mathematics) Content (media) Square number Mereology Numerical analysis Element (mathematics) Stability theory
Torus Point (geometry) Functional (mathematics) Group action Cone penetration test Sigma-algebra Variety (linguistics) Uniqueness quantification Open set Quadratic form Element (mathematics) Natural number Modulform Right angle Spectrum (functional analysis) Spacetime
Cone penetration test Algebraic closure Variety (linguistics) Multiplication sign Musical ensemble Open set Line (geometry) Associative property Orbit
Multiplication sign Moment (mathematics) Line (geometry) Physical system
Sigma-algebra Multiplication sign Expression Sheaf (mathematics) Special functions Product (business) Spacetime Hand fan
Point (geometry) Covering space Closed set Proper map Set theory Spacetime Condition number
Pairwise comparison Group action Root Variety (linguistics) Projective plane Körper <Algebra> Inverse element Limit (category theory) Spacetime 2 (number) Hand fan
Point (geometry) Axiom of choice Group action Perfect group Variety (linguistics) Characteristic polynomial Propositional formula Open set Proper map Pi Diagram Körper <Algebra> Fiber (mathematics) Covering space Multiplication Theory of relativity Surface Projective plane Neighbourhood (graph theory) Basis <Mathematik> Total S.A. Limit (category theory) Cartesian coordinate system Approximation Equivalence relation Proof theory Tower Logic Order (biology) Mathematical singularity Right angle Spacetime
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