Solid locally analytic representations of -adic Lie groups

We develop the theory of locally analytic representations of compact p 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 soli...

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Bibliographic Details
Published in:Representation theory 2022-08, Vol.26 (31), p.962-1024
Main Authors: Rodrigues Jacinto, Joaquín, Rodríguez Camargo, Juan
Format: Article
Language:English
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Summary:We develop the theory of locally analytic representations of compact p 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.
ISSN:1088-4165
1088-4165
DOI:10.1090/ert/615