Seminar über arithmetische Geometrie - Einzelansicht

In this seminar we will study the classical theory, as well as a condensed development, of lo-cally analytic representations. Locally analytic representations of p-adic Lie groups play vital roles for the p-adic Langlands correspondence and its applications. Schneider and Teitelbaum laid both the functional analytic and algebraic foundations for the theory of locally analytic representations in a series of works (e.g., [4, 5]). However, certain inconveniences still remain in the classical theory (for example when considering cohomologies). Condensed mathematics of Scholze and Clausen provides a new approach to deal with vector spaces, algebras, and modules that carry a topology, which particularly include those in the theory of locally analytic representations. Us-ing condensed mathematics, Rodrigues Jacinto and Rodríguez Camargo rebuilt the foundations of locally analytic representation theory in [2].
The first half of this seminar will focus on the classical aspects. Then we will follow [2] to step in the new (and derived) condensed world.

Die organisatorische Vorbesprechung findet in der ersten Semesterwoche zum Seminartermin statt.