Arithmetic cohomology over finite fields and special values of zeta-functions
Number Theory
2007-05-23 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0405164,
title = {Arithmetic cohomology over finite fields and special values of zeta-functions},
author = {Thomas H. Geisser},
journal= {arXiv preprint arXiv:math/0405164},
year = {2007}
}
Comments
28 pages, revised version