Weil-etale cohomology over finite fields
Number Theory
2007-05-23 v1 Algebraic Geometry
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.
Cite
@article{arxiv.math/0404425,
title = {Weil-etale cohomology over finite fields},
author = {Thomas H. Geisser},
journal= {arXiv preprint arXiv:math/0404425},
year = {2007}
}
Comments
Revised version