دانلود کتاب The p-adic Simpson correspondence

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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