The p-adic monodromy theoremMPIM

by Juan Esteban Rodríguez Camargo (MPIM)

Friday May 2, 2025, 2:05 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Arithmetic Geometry and Representation Theory

In this talk I will discuss a new proof of the p-adic monodromy theorem in p-adic Hodge theory using the theory of diamonds and Analytic Geometry à la Clausen and Scholze. This new perspective does not use explicitly  the classical theory of p-adic differential equations but the geometric aspects of Fargues-Fontaine curves and properties of the Fargues-Fontaine de Rham stack. If time permits I will mention the relation of this theory with Hyodo-Kato cohomology. 

This is based on works in progress with Johannes Anschütz, Guido Bosco, Arthur-Cesar Le Bras  and Peter Scholze.