Weil-etale cohomology over finite fields

Details Weil-etale cohomology over finite fields Weil-etale cohomology over finite fields

2004-04-23

arxiv.org/abs/math/0404425v1

Mathematics

Number Theory

Revised version

Scientific paper

We calculate the total derived functor for the map from the Weil-etale site introduced by Lichtenbaum to the etale site for varieties over finite fields. In particular, there is a long exact sequence relating Weil-etale cohomology and etale cohomology. In the second half of the paper, we apply this to study the Weil-etale cohomology of the motivic complex for smooth and projective varieties. These groups are expected to be finitely generated, to give an integral model for l-adic cohomology, and to be related to special values of the zeta function. We give necessary and sufficient conditions for this to hold, and examples.

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