Rigid Cohomology

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

Bernard Le Stum (Author)

9780521875240, Cambridge University Press

Hardback, published 6 September 2007

336 pages, 2 b/w illus.
22.9 x 16.1 x 2.3 cm, 0.61 kg

'… a very nice book, poised to play a role of considerable importance in the literature. Its style is a bit terse but this should be no problem for the reader coming to this field, whose very interest in this fascinating subject bespeaks a commensurate maturity. This brand new book obviously fills an important niche.' MAA Reviews

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 sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas.

Introduction
1. Prologue
2. Tubes
3. Strict neighborhoods
4. Calculus
5. Overconvergent sheaves
6. Overconvergent calculus
7. Overconvergent isocrystals
8. Rigid cohomology
9. Epilogue
Index
Bibliography.

Subject Areas: Topology [PBP], Number theory [PBH]