Previous Special Year Seminar

Some automorphic forms, despite the fact they are algebraic, do not have any interpretation as cohomology classes on a Shimura variety: therefore nothing is known at present on their expected arithmetic properties. I shall explain how such forms...

Let F be a locally compact non-Archimedean field, p its residue characteristic and G a connected reductive algebraic group over F . The classical Satake isomorphism describes the Hecke algebra (over the field of complex numbers) of double classes in...

I will outline the proof of various cases of the local-global compatibility statement alluded to in the title, and also explain its applications to the Fontaine--Mazur conjecture, and to a conjecture of Kisin.

I will outline the proof of various cases of the local-global compatibility statement alluded to in the title, and also explain its applications to the Fontaine—Mazur conjecture, and to a conjecture of Kisin.

We will discuss a generalisation of Serre's conjecture on the possible weights of modular mod p Galois representations for a broad class of reductive groups. In good cases (essentially when the Galois representation is tamely ramified at p) the...

The usual Katz-Mazur model for the modular curve X(p^n) has horribly singular reduction. For large n there isn't any model of X(p^n) which has good reduction, but after extending the base one can at least find a semistable model, which means that...

Let p and l be two distinct prime numbers, and fix a positive integer d . I will explain how the F_l-cohomology complex of the Lubin-Tate tower of height d of a p-adic field K realizes mod l versions of both the semi-simple Langlands correspondence...