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Weil-etale cohomology over finite fields

Thomas H. Geisser
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Abstract

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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Thomas H. Geisser. 2004-04-23. Weil-etale cohomology over finite fields. https://arxiv.org/abs/math/0404425

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