國立虎尾科技大學 |

Rigid cohomology /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Rigid cohomology // Bernard Le Stum.
作者:	Le Stum, Bernard,
面頁冊數:	1 online resource (xv, 319 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Homology theory. -
電子資源:	https://doi.org/10.1017/CBO9780511543128
ISBN:	9780511543128 (ebook)

Rigid cohomology /
Le Stum, Bernard,

Rigid cohomology /Bernard Le Stum. - 1 online resource (xv, 319 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;172. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Alice and Bob1.1

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.

ISBN: 9780511543128 (ebook)Subjects--Topical Terms:

682984
Homology theory.

LC Class. No.: QA612.3 / .L4 2007

Dewey Class. No.: 514.23

Rigid cohomology /
LDR:03588nam a2200301 i 4500 001 1124576
003 UkCbUP
005 20151005020621.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 240926s2007||||enk o ||1 0|eng|d
020 $a 9780511543128 (ebook)
020 $z 9780521875240 (hardback)
035 $a CR9780511543128
040 $a UkCbUP $b eng $e rda $c UkCbUP
050 0 0 $a QA612.3 $b .L4 2007
082 0 4 $a 514.23 $2 22
100 1 $a Le Stum, Bernard, $e author. $3 1442184
245 1 0 $a Rigid cohomology / $c Bernard Le Stum.
264 1 $a Cambridge : $b Cambridge University Press, $c 2007.
300 $a 1 online resource (xv, 319 pages) : $b digital, PDF file(s).
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
490 1 $a Cambridge tracts in mathematics ; $v 172
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $g 1.1 $t Alice and Bob $g 1 -- $g 1.2 $t Complexity $g 2 -- $g 1.3 $t Weil conjectures $g 3 -- $g 1.4 $t Zeta functions $g 4 -- $g 1.5 $t Arithmetic cohomology $g 5 -- $g 1.6 $t Bloch-Ogus cohomology $g 6 -- $g 1.7 $t Frobenius on rigid cohomology $g 7 -- $g 1.8 $t Slopes of Frobenius $g 8 -- $g 1.9 $t The coefficients question $g 9 -- $g 1.10 $t F-isocrystals $g 9 -- $g 2 $t Tubes $g 12 -- $g 2.1 $t Some rigid geometry $g 12 -- $g 2.2 $t Tubes of radius one $g 16 -- $g 2.3 $t Tubes of smaller radius $g 23 -- $g 3 $t Strict neighborhoods $g 35 -- $g 3.1 $t Frames $g 35 -- $g 3.2 $t Frames and tubes $g 43 -- $g 3.3 $t Strict neighborhoods and tubes $g 54 -- $g 3.4 $t Standard neighborhoods $g 65 -- $g 4 $t Calculus $g 74 -- $g 4.1 $t Calculus in rigid analytic geometry $g 74 -- $g 4.3 $t Calculus on strict neighborhoods $g 97 -- $g 4.4 $t Radius of convergence $g 107 -- $g 5 $t Overconvergent sheaves $g 125 -- $g 5.1 $t Overconvergent sections $g 125 -- $g 5.2 $t Overconvergence and abelian sheaves $g 137 -- $g 5.3 $t Dagger modules $g 153 -- $g 5.4 $t Coherent dagger modules $g 160 -- $g 6 $t Overconvergent calculus $g 177 -- $g 6.1 $t Stratifications and overconvergence $g 177 -- $g 6.2 $t Cohomology $g 184 -- $g 6.3 $t Cohomology with support in a closed subset $g 192 -- $g 6.4 $t Cohomology with compact support $g 198 -- $g 6.5 $t Comparison theorems $g 211 -- $g 7 $t Overconvergent isocrystals $g 230 -- $g 7.1 $t Overconvergent isocrystals on a frame $g 230 -- $g 7.2 $t Overconvergence and calculus $g 236 -- $g 7.3 $t Virtual frames $g 245 -- $g 7.4 $t Cohomology of virtual frames $g 251 -- $g 8 $t Rigid cohomology $g 264 -- $g 8.1 $t Overconvergent isocrystal on an algebraic variety $g 264 -- $g 8.2 $t Cohomology $g 271 -- $g 8.3 $t Frobenius action $g 286 -- $g 9.1 $t A brief history $g 299 -- $g 9.2 $t Crystalline cohomology $g 300 -- $g 9.3 $t Alterations and applications $g 302 -- $g 9.4 $t The Crew conjecture $g 303 -- $g 9.5 $t Kedlaya's methods $g 304 -- $g 9.6 $t Arithmetic D-modules $g 306 -- $g 9.7 $t Log poles $g 307.
520 $a 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.
650 0 $a Homology theory. $3 682984
776 0 8 $i Print version: $z 9780521875240
830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511543128