On the p-adic Hodge structure of completed cohomology of modular curves II

Abstract: Let $p$ be a prime. I plan to explain how to read the $p$-adic Hodge structure of the $p$-adically completed cohomology of modular curves by studying the $p$-adic geometry of the modular curves at infinite level. One main tool is the relative Sen theory (also called $p$-adic Simpson correspondence) which provides a first-order differential equation and allows us to apply differential operators pulled back from the flag variety along the Hodge-Tate period map.

Lecture (1): Hodge-Tate structure Lecture (2): de Rham structure

If time permits, I will also discuss several applications.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.