| Description |
1 online resource (xv, 319 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Cambridge tracts in mathematics ; 172
|
|
Cambridge tracts in mathematics ; 172.
|
| Bibliography |
Includes bibliographical references and index. |
| Summary |
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. |
| 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 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 Crew conjecture 303 -- 9.5 Kedlaya's methods 304 -- 9.6 Arithmetic D-modules 306 -- 9.7 Log poles 307. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Homology theory.
|
|
Homology theory. |
| Genre/Form |
Electronic books.
|
|
Electronic books.
|
| Other Form: |
Print version: Le Stum, Bernard. Rigid cohomology. Cambridge : Cambridge University Press, 2007 9780521875240 (DLC) 2008530054 (OCoLC)132298497 |
| ISBN |
9780511342554 (electronic book) |
|
0511342551 (electronic book) |
|
9780511340918 (ebook ; ebrary) |
|
0511340915 (ebook ; ebrary) |
|
9780521875240 (hardback) |
|
0521875242 (hardback) |
|
