TY  - BOOK
AU  - Le Stum,Bernard
TI  - Rigid cohomology
T2  - Cambridge tracts in mathematics
SN  - 9780511543128 (ebook)
AV  - QA612.3 .L4 2007
U1  - 514.23 22
PY  - 2007///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Homology theory
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 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
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511543128
ER  -