Weil-étale cohomology
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In (date), a new Grothendieck topology was introduced by S. Lichtenbaum, defined on the category of schemes of finite type over a finite field. Its construction bears the same relation to the étale topology as the Weil group does to the Galois group.
The Weil-étale site
Weil-étale sheaves and cohomology
The Lichtenbaum conjectures
It was conjectured that the Weil-étale cohomology groups could be used in computing values of zeta functions.
References
- Lichtenbaum, Stephen. (date) The Weil-Étale Topology, (preprint?).
- Lichtenbaum, Stephen. (2005) The Weil-Étale Topology for Number Rings, (preprint?).
- Geisser, Thomas. Weil-Étale Cohomology over Finite Fields
- Geisser, Thomas. Motivic Weil-Étale Cohomology