# GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR

**Topic: **Completed Cohomology of Shimura Curves and a p-Adic Jacquet-Langlands Correspondence

**Speaker: **James Newton

**Affiliation: **Member, School of Mathematics

**Date & Time: **Wednesday February 9th, 2011, 2:15pm - 3:15pm

**Location: **S-101

**Video:** https://video.ias.edu/galois/newton

In this talk, I will describe a construction of a geometric realisation of a p-adic Jacquet-Langlands correspondence for certain forms of GL(2) over a totally real field. The construction makes use of the completed cohomology of Shimura curves, and a study of the bad reduction of Shimura curves due to Rajaei (generalising work of Ribet for GL(2) over the rational numbers). Along the way I will also describe a p-adic analogue of Mazur's principle in this setting.