Solid locally analytic representations of \(p\)-adic Lie groups

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 t...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Joaquín Rodrigues Jacinto, Juan Esteban Rodríguez Camargo
Format: Article
Language:English
Subjects:
Homology
Isomorphism
Lie groups
Mathematical analysis
Representations
Vectors (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:2331-8422