Notes on p-adic hodge theory
WebClassical Hodge theory studies the relation between singular and de Rham cohomology for complex algebraic varieties. By analogy, p-adic Hodge theory studies the relation between different cohomology theories for p-adic varieties (etale, de … WebThe general themes of p-adic Hodge theory are: (1) To construct a dictionary between certain p-adic representations and certain semilin- ear algebraic objects. un (2) Change base field to Qdp . un un Since Qp is not p-adically complete …
Notes on p-adic hodge theory
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Webp (Γ K). Proof. Let V and W be B-admissible representations. Suppose that f∈Hom Q p [Γ K](V,W) induces a zero map D B(V) →D B(W). Then f induces a zero map V⊗ Q p B→W⊗ Q p Bby Theorem 1.1, which means that fmust be a zero map. We thus find that the functorD B is faithful on RepB Q p (Γ K). It remains to verify that D Bis exact on ... Weba p-adic field. Remark 2.3. The fraction field ofW(F p) is the p-adic completion of the maximal unramified extension of Q p. Hence it is a p-adic field which is not an algebraic extension ofQ p. For the rest of this week, let Kbe p-adic field with abosolute Galois group Γ K. Let m, kbe maximum ideal/residue field ofO K.
http://www-personal.umich.edu/~ahorawa/math_679_p-adic_Hodge.pdf Web1. A working knowledge of the main techniques/results in p-adic Hodge theory 2. Familiarity with the semilinear algebra objects appearing in the theory 3. An understanding of the connections to important problems in algebraic number theory . Schedule: Weeks 1-4: Introduction to Fontaine’s theory, Hodge -Tate and De Rham theory
WebApr 1, 2024 · The proof uses p-adic Simpson and Riemann–Hilbert correspondences of Diao, Lan, Liu, and Zhu and the Sen operator on the decompletions of those developed by Shimizu. Along the way, we observe that a p-adic local system on a smooth geometrically connected algebraic variety over K is Hodge–Tate if its stalk at one closed point is a … WebAN INTRODUCTION TO p-ADIC HODGE THEORY DENIS BENOIS Abstract.These notes provide an introduction to p-adic Hodge theory. They are based on the series of lectures …
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WebIn mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields with residual characteristic p … rdu to cleveland ohioWebThe proceedings volume is the first of three dedicated to p-adic Hodge theory related to the research presented at the 2024 Simons Symposium on p-adic Hodge theory. It features … rdu to csgWebOct 5, 2014 · Vector bundles on curves and p-adic Hodge theory; By Laurent Fargues, Institut de Mathématiques de Jussieu, Paris, Jean-Marc Fontaine, Université Paris Sud Edited by Fred Diamond, King's College London, Payman L. Kassaei, King's College London, Minhyong Kim, University of Oxford; Book: Automorphic Forms and Galois Representations how to spell sownWebThe general themes of p-adic Hodge theory are: (1)To construct a dictionary between certain p-adic representations and certain semilin-ear algebraic objects. (2)Change base eld to Qdun p. Since Qun p is not p-adically complete any more, we need to work with Qdun p … rdu to daytona beachWebINTEGRAL P-ADIC HODGE THEORY, TALK 2 (PERFECTOID RINGS, A inf AND THE PRO-ÉTALE SITE) POL VAN HOFTEN (NOTES BY JAMES NEWTON) 1. Witt vectors, A inf and integral perfectoid rings The first part of the talk will cover Witt vectors, A inf and integral perfectoid rings,followingsection3of[1]. rdu to cleveland nonstopWebThe general themes of p-adic Hodge theory are: 1.To construct a dictionary between certain p-adic representations and certain semilinear algebraic objects. 2.Change base field … how to spell sparkyWebNov 30, 2024 · This Special Issue focuses on the applications of the p-adic analysis and q-calculus to various fields of number theory that deal mainly with mathematical analysis of functions of p-adic numbers in mathematics and the theory of p-adic strings and quantum mechanics, and the theory of complex disordered systems-spin glasses in physics. how to spell sophia in korean