|GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR|
|Topic:||Completed Cohomology of Shimura Curves and a p-Adic Jacquet-Langlands Correspondence|
|Affiliation:||Member, School of Mathematics|
|Date:||Wednesday, February 9|
|Time/Room:||2:15pm - 3:15pm/S-101|
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.