The p-adic Simpson correspondence

Contents
Foreword
I. Representations of the fundamental group and the
torsor of deformations. An overview
I.1 Introduction
I.2 Notation and conventions
I.3 Small generalized representations
I.4 The torsor of deformations
I.5 Faltings ringed topos
I.6 Dolbeault modules
II. Representations of the fundamental group and the torsor of deformations. Local study
II.1 Introduction
II.2 Notation and conventions
II.3 Results on continuous cohomology of profinite groups
II.4. Objects with group actions
II.5 Logarithmic geometry lexicon
II.6 Faltings’ almost purity theorem
II.7 Faltings extension
II.8 Galois cohomology
II.9 Fontaine p-adic infinitesimal thickenings
II.10 Higgs–Tate torsors and algebras
II.11 Galois cohomology II
II.12 Dolbeault representations
II.13 Small representations
II.14 Descent of small representations and applications
II.15 Hodge–Tate representations
III. Representations of the fundamental group and the torsor
of deformations. Global aspects
III.1 Introduction
III.2 Notation and conventions
III.3 Locally irreducible schemes
III.4 Adequate logarithmic schemes
III.5 Variations on the Koszul complex
III.6 Additive categories up to isogeny
III.7 Inverse systems of a topos
III.8 Faltings ringed topos
III.9 Faltings topos over a trait
III.10 Higgs–Tate algebras
III.11 Cohomological computations
III.12 Dolbeault modules
III.13 Dolbeault modules on a small affine scheme
III.14 Inverse image of a Dolbeault module under an étale morphism
III.15 Fibered category of Dolbeault modules
IV. Cohomology of Higgs isocrystals
IV.1 Introduction
IV.2 Higgs envelopes
IV.3 Higgs isocrystals and Higgs crystals
IV.4 Cohomology of Higgs isocrystals
IV.5 Representations of the fundamental group
IV.6 Comparison with Faltings cohomology
V. Almost étale coverings
V.1 Introduction
V.2 Almost isomorphisms
V.3 Almost finitely generated projective modules
V.4 Trace
V.5 Rank and determinant
V.6 Almost flat modules and almost faithfully flat modules
V.7 Almost étale coverings
V.8 Almost faithfully flat descent I
V.9 Almost faithfully flat descent II
V.11 Group cohomology of discrete A-G-modules
V.10 Liftings
V.12 Galois cohomology
VI. Covanishing topos and generalizations
VI.1 Introduction
VI.2 Notation and conventions
VI.3 Oriented products of topos
VI.4 Covanishing topos
VI.5 Generalized covanishing topos
VI.6 Morphisms with values in a generalized covanishing topos
VI.7 Ringed total topos
VI.8 Ringed covanishing topos
VI.9 Finite étale site and topos of a scheme
VI.10 Faltings site and topos
VI.11 Inverse limit of Faltings topos
Facsimile : A p-adic Simpson correspondence
1. Introduction
2. Generalised representations
3. The local structure of generalised representations
4. Globalisation
5. Examples and open questions
References
Bibliography
Indexes
A P-adic Simpson Correspondence II: Small
Representations
1. Introduction
2. Berger's rings in higher dimensions
3. Bundles with a singular connection
4. Examples
References