English

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 pp-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 \Gm\G_m on a smooth, proper curve with a rational point. This last theorem is analogous to, and implies, a classical duality theorem for such curves.

Keywords

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}
}
R2 v1 2026-06-21T19:43:03.364Z