The p-adic Simpson correspondence /

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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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Abbes, Ahmed (Author), Gros, Michel, 1956- (Author), Tsuji, Takeshi, 1967- (Author)
Format: Electronic eBook
Language:Inglés
Published: Princeton : Princeton University Press, 2016.
Series:Annals of mathematics studies ; no. 193.
Subjects:
Group theory.
p-adic groups.
Geometry, Algebraic.
Théorie des groupes.
Groupes p-adiques.
Géométrie algébrique.
MATHEMATICS > Algebra > Intermediate.
MATHEMATICS > Algebra > General.
Geometry, Algebraic
Group theory
p-adic groups
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.
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.
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.
Online Access:Texto completo
Table of 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 étale coverings
  • Chapter VI. Covanishing topos and generalizations
  • Facsimile : A p-adic Simpson correspondence
  • Bibliography
  • Indexes.

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