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

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

2004-05-10

arxiv.org/abs/math/0405164v2

Mathematics

Number Theory

28 pages, revised version

Scientific paper

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.

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