Author(s): Ahmed Abbes; Michel Gros; Takeshi Tsuji
Series: Annals of Mathematics Studies 193
Publisher: Princeton University Press
Year: 2016
Language: English
Pages: 606
Tags: Hodge theory; p-adic fields; Arithmetical algebraic geometry
Contents......Page 2
Foreword......Page 4
I.1. Introduction......Page 7
I.2. Notation and conventions......Page 9
I.3. Small generalized representations......Page 11
I.4. The torsor of deformations......Page 12
I.5. Faltings ringed topos......Page 19
I.6. Dolbeault modules......Page 25
II.1. Introduction......Page 33
II.2. Notation and conventions......Page 34
II.3. Results on continuous cohomology of profinite groups......Page 41
II.4. Objects with group actions......Page 56
II.5. Logarithmic geometry lexicon......Page 69
II.6. Faltings’ almost purity theorem......Page 77
II.7. Faltings extension......Page 90
II.8. Galois cohomology......Page 104
II.9. Fontaine p-adic infinitesimal thickenings......Page 116
II.10. Higgs–Tate torsors and algebras......Page 126
II.11. Galois cohomology II......Page 138
II.12. Dolbeault representations......Page 149
II.13. Small representations......Page 159
II.14. Descent of small representations and applications......Page 172
II.15. Hodge–Tate representations......Page 181
III.1. Introduction......Page 185
III.2. Notation and conventions......Page 186
III.3. Locally irreducible schemes......Page 190
III.4. Adequate logarithmic schemes......Page 191
III.5. Variations on the Koszul complex......Page 196
III.6. Additive categories up to isogeny......Page 200
III.7. Inverse systems of a topos......Page 209
III.8. Faltings ringed topos......Page 217
III.9. Faltings topos over a trait......Page 228
III.10. Higgs–Tate algebras......Page 235
III.11. Cohomological computations......Page 256
III.12. Dolbeault modules......Page 272
III.13. Dolbeault modules on a small affine scheme......Page 290
III.14. Inverse image of a Dolbeault module under an étale morphism......Page 296
III.15. Fibered category of Dolbeault modules......Page 305
IV.1. Introduction......Page 313
IV.2. Higgs envelopes......Page 319
IV.3. Higgs isocrystals and Higgs crystals......Page 356
IV.4. Cohomology of Higgs isocrystals......Page 375
IV.5. Representations of the fundamental group......Page 389
IV.6. Comparison with Faltings cohomology......Page 408
V.1. Introduction......Page 455
V.2. Almost isomorphisms......Page 456
V.3. Almost finitely generated projective modules......Page 458
V.4. Trace......Page 459
V.5. Rank and determinant......Page 461
V.6. Almost flat modules and almost faithfully flat modules......Page 465
V.7. Almost étale coverings......Page 467
V.8. Almost faithfully flat descent I......Page 470
V.9. Almost faithfully flat descent II......Page 473
V.10. Liftings......Page 477
V.11. Group cohomology of discrete A-G-modules......Page 484
V.12. Galois cohomology......Page 487
VI.1. Introduction......Page 491
VI.2. Notation and conventions......Page 499
VI.3. Oriented products of topos......Page 500
VI.4. Covanishing topos......Page 508
VI.5. Generalized covanishing topos......Page 517
VI.6. Morphisms with values in a generalized covanishing topos......Page 533
VI.7. Ringed total topos......Page 538
VI.8. Ringed covanishing topos......Page 543
VI.9. Finite étale site and topos of a scheme......Page 548
VI.10. Faltings site and topos......Page 556
VI.11. Inverse limit of Faltings topos......Page 576
Bibliography......Page 583
Indexes......Page 586
A p-adic Simpson correspondence......Page 591
