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Annals of Mathematics Studies: P-Adic Simpson Correspondence by Michel Gros, Takeshi Tsuji and Ahmed Abbes (2016, Hardcover)

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About this product

Product Identifiers

PublisherOxford University Press, Incorporated

ISBN-100691170282

ISBN-139780691170282

eBay Product ID (ePID)219266640

Product Key Features

Number of Pages616 Pages

Publication NameP-Adic Simpson Correspondence

LanguageEnglish

Publication Year2016

SubjectGroup Theory, Algebra / Linear, Algebra / General, Geometry / Algebraic, Mathematical Analysis

TypeTextbook

AuthorMichel Gros, Takeshi Tsuji, Ahmed Abbes

Subject AreaMathematics

SeriesAnnals of Mathematics Studies

FormatHardcover

Dimensions

Item Height1.5 in

Item Weight43.1 Oz

Item Length10.2 in

Item Width7.2 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2015-031778

TitleLeadingThe

Dewey Edition23

ReviewsThe authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts. ---Gerd Faltings, Zentralblatt MATH, "The authors give a very detailed introduction to the theory, smoothing out some difficulties by introducing new concepts." --Gerd Faltings, Zentralblatt MATH

Series Volume Number193

IllustratedYes

Dewey Decimal512/.2

SynopsisThe p -adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p -adic representations of the fundamental group of a proper smooth variety over a p -adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p -adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p -adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p -adic Hodge theory. The reader will find a concise 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., The p -adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p -adic representations of the fundamental group of a proper smooth variety over a p -adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p -adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p -adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p -adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost tale 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.

LC Classification NumberQA179.A23 2016