Arithmetic cohomology over finite fields and special values of zeta-functions, by Thomas Geisser

[The original version submitted May 15, 2004, has been replaced March 23, 2005.]

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.


Thomas Geisser <geisser@ms.u-tokyo.ac.jp>