Notes on p-adic hodge theory

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August undefined, 2024

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 … Webp-adic Hodge theory serves as an essential ingredient. Our switch in notation hopefully emphasizes this point without causing too much confusion. Part 1. The proof by Faltings Notations (for Faltings’s proof). K=Q denotes a number eld. Salways denotes a nite set of places of K, and is often assumed to contain all

MATH 679: INTRODUCTION TO p-ADIC HODGE …

WebDownload or read book p-adic Hodge Theory written by Bhargav Bhatt and published by Springer Nature. This book was released on 2024-06-15 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains articles related to the research presented at the 2024 Simons Symposium on p-adic Hodge theory. Webconcise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos. crystal cards meanings

(PDF) P Adic Hodge Theory eBook Online eBook House Library

WebIn this volume, Perrin-Riou presents a theory of p-adic L-functions coming directly from p-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of p-adic L-functions via the arithmetic theory and a conjectural deﬁnition of the p-adic L-function via its special values. WebIn the proof of many known cases (especially in work of Kisin), p-adic Hodge theory 3 Of course, we will also discuss crystalline representations and Hodge-Tate representations 4 Note that Taniyama-Shimura conjecture is the only the special case of Conjecture 1.5 for WebJan 21, 2024 · p-adic Hodge theory is the study of properties of p-adic (étale, de Rham, logarithmic cristalline) cohomology (and motives) of non-archimedean analytic spaces. … crystal cards sun lakes az

Continuous K-theory and cohomology of rigid spaces

Webp+q=n V p;qsuch that Vp;q= Vq;p. The Hodge decomposition is proved using transcendental methods (such as the use of a K¨ahler metric). More generally, such a decomposition holds for compact K¨ahler manifolds. One of the goals of p-adic Hodge theory is to prove similar results in the case where Cis replaced instead by a p-adic ﬁeld F. WebSome lecture notes on p -adic Hodge theory, from a course I taught with Olivier Brinon at the 2009 CMI summer school on Galois representations. It is undergoing regular revision; not yet in final form (so corrections … crystal cards \u0026 crystal art kitsWebOur goal in this section is to give a rough idea of what p-adic Hodge theory is about. By nature, p-adic Hodge theory has two sides of the story, namely the arithmetic side and … crystal card kit

"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. " - Notes on p-adic hodge theory

Notes on p-adic hodge theory

-adic Hodge theory - University of Chicago

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 ... WebThe 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 …

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WebAug 2, 2016 · Notes on the A_inf-cohomology of Integral p-adic Hodge theory M. Morrow Published 2 August 2016 Mathematics arXiv: Algebraic Geometry We present a detailed overview of the construction of the A_inf-cohomology theory from the preprint "Integral p-adic Hodge theory", joint with B. Bhatt and P. Scholze. WebFor instance, p-adic Hodge theory, which relates p-adic ´etale cohomology groups to de Rham cohomology is clearly a prime example of such a theory. In the case of ρX, however, because one is dealing with a highly nonabelian object such as ΔX, it is not immediately clear what the appropriate Hodge theory should be. One

WebAN INTRODUCTION TO THE THEORY OF p-ADIC REPRESENTATIONS 5 I.2.2. Deﬁnitions. — A p-adic representation V of GK is a ﬁnite dimensional Qp-vector space with a continuous linear action of GK. The dimension of V as a Qp-vector space will always be denoted by d. Here are some examples of p-adic representations: 1. WebAug 2, 2016 · Abstract: We present a detailed overview of the construction of the A_inf-cohomology theory from the preprint "Integral p-adic Hodge theory", joint with B. Bhatt …

WebAug 2, 2016 · Title: Notes on the A_inf-cohomology of Integral p-adic Hodge theory. Authors: Matthew Morrow. Download PDF Abstract: We present a detailed overview of the construction of the A_inf-cohomology theory from the preprint "Integral p-adic Hodge theory", joint with B. Bhatt and P. Scholze. We focus particularly on the p-adic analogue of …

WebINTEGRAL p-ADIC HODGE THEORY, ALKT 7 (BREUIL KISIN MODULES) TOBY GEE (NOTES BY JAMES NEWTON) 1. Introduction This talk is going to discuss section 4.1 of [2]. ... Note that each localisation A p is a dvr. Now you can check that, for M torsion free, we get M = T pht 1 M and M = T p ht 1 M p. It follows that Mis re exive if and only if M= T crystal cards with meaningsWebNov 10, 2024 · Anyway there are many introductory notes on p -adic Hodge theory, written by various specialists of the topic, usually available on their websites. These are a good resource. Note however that you probably cannot avoid some sort of notion in differential geometry. E.g. you will have difficulty building intuition about de Rham representations. crystal cardwell mdhttp://www-personal.umich.edu/~serinh/Notes%20on%20p-adic%20Hodge%20theory.pdf crystal cards printablehttp://math.stanford.edu/~conrad/ dvr logo change software downloadWebApr 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 … crystal cards \\u0026 crystal art kitshttp://www-personal.umich.edu/~ahorawa/math_679_p-adic_Hodge.pdf crystal care and chargingWebJan 21, 2024 · p-adic Hodge theoryis the study of properties of p-adic (étale, de Rham, logarithmic cristalline) cohomology(and motives) of non-archimedean analytic spaces. The pp-adic Hodge structure of a (proper or semi-stably compactified) p-adic analytic variety is essentially given by a relation between three important invariants of the given variety: crystal care center of franklin furnace