Solid locally analytic representations of 𝑝-adic Lie groups

Rodrigues Jacinto, Joaquín; Rodríguez Camargo, Juan

doi:10.1090/ert/615

Solid locally analytic representations of $p$-adic Lie groups
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by Joaquín Rodrigues Jacinto and Juan Esteban Rodríguez Camargo

Represent. Theory 26 (2022), 962-1024

DOI: https://doi.org/10.1090/ert/615

Published electronically: August 31, 2022

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Abstract:

We develop the theory of locally analytic representations of compact $p$-adic Lie groups from the perspective of the theory of condensed mathematics of Clausen and Scholze. As an application, we generalise Lazard’s isomorphisms between continuous, locally analytic and Lie algebra cohomology to solid representations. We also prove a comparison result between the group cohomology of a solid representation and of its analytic vectors.

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