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arXiv · 2402.05565

Duality for condensed cohomology of the Weil group of a p-adic field

Marco Artusa
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Abstract

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate Duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups.

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Marco Artusa. 2024-02-08. Duality for condensed cohomology of the Weil group of a p-adic field. https://doi.org/10.4171/dm/977

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