arXiv Analytics

Sign in

arXiv:math/0405164 [math.NT]AbstractReferencesReviewsResources

Arithmetic cohomology over finite fields and special values of zeta-functions

Thomas H. Geisser

Published 2004-05-10, updated 2005-03-23Version 2

We construct a cohomology theory with compact support H^i_c(X_ar,Z(n))$ for separated schemes of finite type over a finite field, which should play a role analog to Lichtenbaum's Weil-etale cohomology groups for smooth and projective schemes. In particular, if Tate's conjecture holds and rational and numerical equivalence agree up to torsion, then the groups H^i_c(X_ar,Z(n)) are finitely generated, form an integral version of l-adic cohomology with compact support, and admit a formula for the special values of the zeta-function of X.

Comments: 28 pages, revised version
Categories: math.NT, math.AG
Related articles: Most relevant | Search more
arXiv:math/0511115 [math.NT] (Published 2005-11-04, updated 2006-02-15)
On the faithfulness of parabolic cohomology as a Hecke module over a finite field
arXiv:math/0412367 [math.NT] (Published 2004-12-18, updated 2005-03-31)
Endomorphism Rings and Isogenies Classes for Drinfeld Modules of Rank 2 Over Finite Fields
arXiv:math/0612147 [math.NT] (Published 2006-12-06)
Counting points on varieties over finite fields of small characteristic

Links

Toolbox