Weil-étale cohomology over finite fields

By Thomas H. Geisser. 2004

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Abstract.We calculate the derived functors Rγ* for the base change γ from the Weil-étale site to the étale site for a variety over a finite field. For smooth and proper varieties, we apply this to express Tate’s conjecture and Lichtenbaum’s conjecture on special values of ζ-functions in terms of Weil-étale cohomology of the motivic complex ℤ(n).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8aef43d712a20129e194a8f9b749f5afd1096e82