Abstract: In joint work with C. Breuil and B. Schraen we prove (under mild additional hypothesis) that p -adic automorphic forms on eigenvarieties for definite unitary groups are classical if their associated p -adic Galois representation is crystalline at places dividing p . In the same setup we further determine all non-classical overconvergent forms of finite slope that give rise to the same Galois representation as a classical automorphic form. These results rely on a close analysis of the local geometry of a space parametrizing p -adic Galois representations with a certain prescribed behaviour at p – so called triangulate representations. We study this geometry by proving that the space is smoothly equivalent to a certain variety showing up in geometric representation theory.
As usual, the seminar will be preceded by various study groups, starting at 1200.
The talks will be preceded by tea/coffee in Imperial’s common room (room 549 Huxley) from 3:30.