Number Theory Seminar

Speaker: Andrea Dotto (Chicago)

Title: Multiplicity one and Breuil--Kisin cohomology of Shimura curves.

Abstract: The multiplicity of Hecke eigenspaces in the mod p cohomology of Shimura curves is a classical invariant which has been computed in significant generality when the group splits at p. These results have recently found interesting applications to the mod p Langlands correspondence for GL_2 over unramified p-adic fields. As a first step towards extending these to nonsplit quaternion algebras, we prove a new multiplicity one theorem in the nonsplit case. The main idea of the proof is to use the Breuil--Kisin module associated to a finite flat model of the cohomology to reduce the problem to a known statement about modular forms on totally definite quaternion algebras.

The talk will take place on Zoom. If you are interested in attending and not on the Number Theory Seminar mailing list, please contact the organizer to obtain the link