2004/04/23 by Thomas Geisser, Thomas H. Geisser, Geisser, Thomas H.
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.NT #msc:11G25 #msc:14F20 #msc:14F42
paper · pdf · doi:10.48550/arxiv.math/0404425
Revised version
arxiv created 2004/04/23 · arxiv updated 2009/12/01
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.