Rigid cohomology /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Le Stum, Bernard
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2007.
Colección:Cambridge tracts in mathematics ; 172.
Temas:
Homology theory.
Homologie.
MATHEMATICS > Topology.
Homology theory
Kristalline Kohomologie
Verallgemeinerung
Acceso en línea:Texto completo
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.

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