Seminar in Algebraic Geometry and Number Theory

Abstract: I will introduce the p-adic local Langlands correspondence for GL(2,Qp), in the forms established by Colmez and Paskunas, and then give an interpretation of it as an embedding of categories (a form of "localization"). Time permitting, I will also discuss formulas for singular cohomology of modular curves that you can get from this, generalizing the usual decomposition of an automorphic representation into its local components.

This is joint work with James Newton and Carl Wang-Erickson.