Abstract: Suppose that ρ is an irreducible automorphic n -dimensional global p -adic Galois representation that is upper-triangular locally at p . In previous work with Breuil we constructed a unitary representation of GLn(Qp) on a p -adic Banach space (depending only on ρ locally at p ) that is an extension of finitely many principal series, and we conjectured that this representation occurs globally in a space of p -adic automorphic forms cut out by ρ . In work in progress we prove many new cases of this conjecture, assuming that ρ is moreover crystalline.
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.