000			03747nam a22003498i 4500
001			CR9780511543128
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2007||||enk o ||1 0|eng|d
020			_a9780511543128 (ebook)
020			_z9780521875240 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA612.3 _b.L4 2007
082	0	4	_a514.23 _222
100	1		_aLe Stum, Bernard, _eauthor.
245	1	0	_aRigid cohomology / _cBernard Le Stum.
264		1	_aCambridge : _bCambridge University Press, _c2007.
300			_a1 online resource (xv, 319 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v172
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_g1.1 _tAlice and Bob _g1 -- _g1.2 _tComplexity _g2 -- _g1.3 _tWeil conjectures _g3 -- _g1.4 _tZeta functions _g4 -- _g1.5 _tArithmetic cohomology _g5 -- _g1.6 _tBloch-Ogus cohomology _g6 -- _g1.7 _tFrobenius on rigid cohomology _g7 -- _g1.8 _tSlopes of Frobenius _g8 -- _g1.9 _tThe coefficients question _g9 -- _g1.10 _tF-isocrystals _g9 -- _g2 _tTubes _g12 -- _g2.1 _tSome rigid geometry _g12 -- _g2.2 _tTubes of radius one _g16 -- _g2.3 _tTubes of smaller radius _g23 -- _g3 _tStrict neighborhoods _g35 -- _g3.1 _tFrames _g35 -- _g3.2 _tFrames and tubes _g43 -- _g3.3 _tStrict neighborhoods and tubes _g54 -- _g3.4 _tStandard neighborhoods _g65 -- _g4 _tCalculus _g74 -- _g4.1 _tCalculus in rigid analytic geometry _g74 -- _g4.3 _tCalculus on strict neighborhoods _g97 -- _g4.4 _tRadius of convergence _g107 -- _g5 _tOverconvergent sheaves _g125 -- _g5.1 _tOverconvergent sections _g125 -- _g5.2 _tOverconvergence and abelian sheaves _g137 -- _g5.3 _tDagger modules _g153 -- _g5.4 _tCoherent dagger modules _g160 -- _g6 _tOverconvergent calculus _g177 -- _g6.1 _tStratifications and overconvergence _g177 -- _g6.2 _tCohomology _g184 -- _g6.3 _tCohomology with support in a closed subset _g192 -- _g6.4 _tCohomology with compact support _g198 -- _g6.5 _tComparison theorems _g211 -- _g7 _tOverconvergent isocrystals _g230 -- _g7.1 _tOverconvergent isocrystals on a frame _g230 -- _g7.2 _tOverconvergence and calculus _g236 -- _g7.3 _tVirtual frames _g245 -- _g7.4 _tCohomology of virtual frames _g251 -- _g8 _tRigid cohomology _g264 -- _g8.1 _tOverconvergent isocrystal on an algebraic variety _g264 -- _g8.2 _tCohomology _g271 -- _g8.3 _tFrobenius action _g286 -- _g9.1 _tA brief history _g299 -- _g9.2 _tCrystalline cohomology _g300 -- _g9.3 _tAlterations and applications _g302 -- _g9.4 _tThe Crew conjecture _g303 -- _g9.5 _tKedlaya's methods _g304 -- _g9.6 _tArithmetic D-modules _g306 -- _g9.7 _tLog poles _g307.
520			_aDating 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	_aHomology theory.
776	0	8	_iPrint version: _z9780521875240
830		0	_aCambridge tracts in mathematics ; _v172.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543128
999			_c517794 _d517792