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
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.