Rigid cohomology / Bernard Le Stum.

Format:

Book

Author/Creator:

Le Stum, Bernard.

Series:

Cambridge tracts in mathematics ; no. 172.

Cambridge tracts in mathematics ; no. 172

Language:

English

Subjects (All):

Homology theory.

Physical Description:

xv, 319 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Summary:

The first book to give a complete treatment of rigid cohomology, from the basics to the very latest developments.

Contents:

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.

Notes:

Includes bibliographical references (pages 310-314) and index.

ISBN:

0521875242

9780521875240

OCLC:

132298497