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

  • Marco Artusa

    Université de Bordeaux, Talence, France
Duality for condensed cohomology of the Weil group of a $p$-adic field cover
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Abstract

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a -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.

Cite this article

Marco Artusa, Duality for condensed cohomology of the Weil group of a -adic field. Doc. Math. 29 (2024), no. 6, pp. 1381–1434

DOI 10.4171/DM/977