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E-BOOK
Title The p-adic Simpson correspondence / Ahmed Abbes, Michel Gros, Takeshi Tsuji.
Imprint Princeton : Princeton University Press, 2016.

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Description 1 online resource
Series Annals of Mathematics Studies ; 193
Annals of mathematics studies ; no. 193.
Bibliog. Includes bibliographical references and index.
Note Available only to authorized UTEP users.
In English.
Print version record.
Subject Group theory.
p-adic groups.
Geometry, Algebraic.
Genre Electronic book.
Electronic books.
Contents Frontmatter -- Contents -- Foreword -- Chapter I. Representations of the fundamental group and the torsor of deformations. An overview -- Chapter II. Representations of the fundamental group and the torsor of deformations. Local study -- Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects -- Chapter IV. Cohomology of Higgs isocrystals -- Chapter V. Almost ├ętale coverings -- Chapter VI. Covanishing topos and generalizations -- Facsimile : A p-adic Simpson correspondence -- Bibliography -- Indexes.
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 ├ętale 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.
Other Author Gros, Michel, 1956- author.
Tsuji, Takeshi, 1967- author.
Other Title Print version: Abbes, Ahmed. P-adic Simpson correspondence 9780691170282