Geodesic
Duality for condensed cohomology of the Weil group of a $p$-adic field
Documenta mathematica, Tome 29 (2024) no. 6, pp. 1381-1434

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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.
DOI : 10.4171/dm/977
Classification : 11S25, 11S31, 14F20, 11F85
Mots-clés : cohomology of condensed groups, condensed mathematics, Weil group, Pontryagin duality, local Tate duality 
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     author = {Marco Artusa},
     title = {Duality for condensed cohomology of the {Weil} group of~a~$p$-adic field},
     journal = {Documenta mathematica},
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     year = {2024},
     doi = {10.4171/dm/977},
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Marco Artusa. Duality for condensed cohomology of the Weil group of a $p$-adic field. Documenta mathematica, Tome 29 (2024) no. 6, pp. 1381-1434. doi: 10.4171/dm/977

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