Franklin

The p-adic Simpson Correspondence (AM-193) / Takeshi Tsuji, Michel Gros, Ahmed Abbes.

Other records:
Author/Creator:
Abbes, Ahmed author.
Publication:
Princeton, NJ : Princeton University Press, [2016]
Series:
Annals of Mathematics Studies ; 226
Format/Description:
Book
1 online resource
Subjects:
Geometry, Algebraic.
Group theory.
p-adic groups.
Language:
In English.
System Details:
Mode of access: Internet via World Wide Web.
text file PDF
Summary:
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 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.
Contents:
Frontmatter
Contents
Foreword
Chapter I. Representations of the fundamental group and the torsor of deformations. An overview / Abbes, Ahmed / Gros, Michel
Chapter II. Representations of the fundamental group and the torsor of deformations. Local study / Abbes, Ahmed / Gros, Michel
Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects / Abbes, Ahmed / Gros, Michel
Chapter IV. Cohomology of Higgs isocrystals / Tsuji, Takeshi
Chapter V. Almost étale coverings / Tsuji, Takeshi
Chapter VI. Covanishing topos and generalizations / Abbes, Ahmed / Gros, Michel
Facsimile : A p-adic Simpson correspondence / Faltings, Gerd
Bibliography
Indexes
Notes:
Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)
Contributor:
Gros, Michel, author.
Tsuji, Takeshi, author.
De Gruyter.
Contained In:
De Gruyter University Press Library.
ISBN:
9781400881239
OCLC:
934626614
Publisher Number:
10.1515/9781400881239 doi
Access Restriction:
Restricted for use by site license.
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