2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70947We 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.Revised versionNumber TheoryAlgebraic Geometry14F20 (Primary) 14F42, 11G25 (Secondary)text