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

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:Wednesday, February 9
Time/Room:2:15pm - 3:15pm/S-101
Video Link: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.