Weil-étale Cohomology over $p$-adic Fields
Abstract
We establish duality results for the cohomology of the Weil group of a $p$-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 $\G_m$ on a smooth, proper curve with a rational point. This last theorem is analogous to, and implies, a classical duality theorem for such curves.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2011
- DOI:
- 10.48550/arXiv.1111.6710
- arXiv:
- arXiv:1111.6710
- Bibcode:
- 2011arXiv1111.6710K
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry