Weil-\'etale Cohomology over $p$-adic Fields
Number Theory
2012-05-30 v3 Algebraic Geometry
Abstract
We establish duality results for the cohomology of the Weil group of a -adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama Duality. We define Weil-smooth cohomology for varieties over local fields, and prove a duality theorem for the cohomology of on a smooth, proper curve with a rational point. This last theorem is analogous to, and implies, a classical duality theorem for such curves.
Cite
@article{arxiv.1111.6710,
title = {Weil-\'etale Cohomology over $p$-adic Fields},
author = {David A. Karpuk},
journal= {arXiv preprint arXiv:1111.6710},
year = {2012}
}