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The p-adic Simpson correspondence / / Ahmed Abbes, Michel Gros, Takeshi Tsuji



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Autore: Abbes Ahmed Visualizza persona
Titolo: The p-adic Simpson correspondence / / Ahmed Abbes, Michel Gros, Takeshi Tsuji Visualizza cluster
Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 2016
Descrizione fisica: 1 online resource (618 p.)
Disciplina: 512/.2
Soggetto topico: Group theory
p-adic groups
Geometry, Algebraic
Soggetto non controllato: Dolbeault generalized representation
Dolbeault module
Dolbeault representation
Faltings cohomology
Faltings extension
Faltings ringed topos
Faltings site
Faltings topos
Galois cohomology
Gerd Faltings
Higgs bundle
Higgs bundles
Higgs crystals
Higgs envelopes
Higgs isocrystal
HiggsДate algebra
HodgeДate representation
HodgeДate structure
HodgeДate theory
Hyodo's theory
Koszul complex
additive categories
adic module
almost faithfully flat descent
almost faithfully flat module
almost flat module
almost isomorphism
almost tale covering
almost tale extension
cohomology
covanishing topos
crystalline-type topos
deformation
discrete AЇ-module
finite tale site
fundamental group
generalized covanishing topos
generalized representation
inverse limit
linear algebra
locally irreducible scheme
morphism
overconvergence
p-adic Hodge theory
p-adic Simpson correspondence
p-adic field
period ring
ringed covanishing topos
ringed total topos
small generalized representation
small representation
solvable Higgs module
tale cohomology
tale fundamental group
torsor
Classificazione: SI 830
Persona (resp. second.): GrosMichel <1956->
TsujiTakeshi <1967->
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- 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
Sommario/riassunto: 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.
Titolo autorizzato: The p-adic Simpson correspondence  Visualizza cluster
ISBN: 1-4008-8123-4
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910797970703321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; no. 193.