Solid locally analytic representations of p-adic Lie groups

2021/10/22 by Joaquín Rodrigues Jacinto, Jacinto, Joaquín Rodrigues, Juan Esteban Rodríguez Camargo +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #advanced mathematical theories #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2110.11916

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.

Cited by

• On the pro-étale cohomology of quotient stacks of Drinfeld spaces
• Locally analytic completed cohomology of Shimura varieties of Hodge type

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• Solid locally analytic representations
• Solid locally analytic representations in mixed characteristic
• Locally analytic vectors in representations of locally p-adic analytic groups
• U(g)-finite locally analytic representations
• A comparison of locally analytic group cohomology and Lie algebra cohomology for p-adic Lie groups