Rigid cohomology
Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the se...
| Otros Autores: | |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press
2007.
|
| Colección: | CUP ebooks.
Cambridge tracts in mathematics ; 172. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b45432612*spi |
Tabla de Contenidos:
- 1.1 Alice and Bob 1
- 1.2 Complexity 2
- 1.3 Weil conjectures 3
- 1.4 Zeta functions 4
- 1.5 Arithmetic cohomology 5
- 1.6 Bloch-Ogus cohomology 6
- 1.7 Frobenius on rigid cohomology 7
- 1.8 Slopes of Frobenius 8
- 1.9 The coefficients question 9
- 1.10 F-isocrystals 9
- 2 Tubes 12
- 2.1 Some rigid geometry 12
- 2.2 Tubes of radius one 16
- 2.3 Tubes of smaller radius 23
- 3 Strict neighborhoods 35
- 3.1 Frames 35
- 3.2 Frames and tubes 43
- 3.3 Strict neighborhoods and tubes 54
- 3.4 Standard neighborhoods 65
- 4 Calculus 74
- 4.1 Calculus in rigid analytic geometry 74
- 4.3 Calculus on strict neighborhoods 97
- 4.4 Radius of convergence 107
- 5 Overconvergent sheaves 125
- 5.1 Overconvergent sections 125
- 5.2 Overconvergence and abelian sheaves 137
- 5.3 Dagger modules 153
- 5.4 Coherent dagger modules 160
- 6 Overconvergent calculus 177
- 6.1 Stratifications and overconvergence 177
- 6.2 Cohomology 184
- 6.3 Cohomology with support in a closed subset 192
- 6.4 Cohomology with compact support 198
- 6.5 Comparison theorems 211
- 7 Overconvergent isocrystals 230
- 7.1 Overconvergent isocrystals on a frame 230
- 7.2 Overconvergence and calculus 236
- 7.3 Virtual frames 245
- 7.4 Cohomology of virtual frames 251
- 8 Rigid cohomology 264
- 8.1 Overconvergent isocrystal on an algebraic variety 264
- 8.2 Cohomology 271
- 8.3 Frobenius action 286
- 9.1 A brief history 299
- 9.2 Crystalline cohomology 300
- 9.3 Alterations and applications 302
- 9.4 The Crew conjecture 303
- 9.5 Kedlaya's methods 304
- 9.6 Arithmetic D-modules 306
- 9.7 Log poles 307.
