Solid locally analytic representations of $p$-adic Lie groups

Abstract: Motivated from the works of Lazard, Schneider-Teitelbaum and Emerton, and from the theory of condensed mathematics developed by Clausen and Scholze, we give new foundations for the theory of locally analytic representations of (compact) $p$-adic Lie groups. In this talk we will discuss how the interpretation of taking analytic vectors à la Emerton shows that the concept of being an analytic representation for some open compact subgroup is the same as being a module over some analytic distribution algebra. This observation algebraizes the theory of locally analytic representations, and some comparison theorems of Lazard and Tamme on continuous - locally analytic - Lie algebra cohomology hold for general solid representations by basic homological algebra arguments. Joint work with Joaquín Rodrigues Jacinto.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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