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

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

James Newton
Member, School of Mathematics
February 9, 2011

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.