On the locally analytic completed cohomology of modular curves

TL;DR

This paper surveys the authors' research on the locally analytic vectors within the completed cohomology of modular curves, highlighting their contributions to understanding the analytic structure of these cohomological spaces.

Contribution

It provides a comprehensive overview of the authors' work on locally analytic vectors in the completed cohomology of modular curves, emphasizing new insights into their structure.

Findings

Characterization of locally analytic vectors in completed cohomology

Connections between cohomology and automorphic representations

Framework for analyzing p-adic properties of modular curves

Abstract

We survey our works on the locally analytic vectors of completed cohomology of modular curves.