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Arithmetic Cohomology Over Finite Fields and Special Values of Zeta-functions by Geisser, Thomas H. is a scholarly article available to read on EtoBox.

What is Arithmetic Cohomology Over Finite Fields and Special Values of Zeta-functions about?

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.

Author

Geisser, Thomas H.

Published

2004

Language

EN