London-Paris Number Theory Seminar

First meeting, Paris, 13/11/2006

The 1st meeting took place on Monday 13th November 2006 in the Institut Henri Poincaré in Paris. The schedule was

9.30-9.45 Gathering at the IHP
9.45-10.00 Brief opening remarks
10.00-11.00 Fred Diamond (King's College London)
The weight part of Serre's conjecture for Hilbert modular forms
Abstract: I will explain the statement of a generalization of Serre's conjecture on modulo p Galois representations to the context of Hilbert modular forms. The emphasis will be on the recipe (conjectured by Buzzard, Jarvis and myself) for the set of possible weights, much of which has now been proved by Gee. I will also discuss some features of the set of weights in some special cases:
1) for representations tamely ramified at primes over p, a phenomenon which was interpreted conceptually and generalized to GLn by Herzig ;
2) for representations that could be called ”moins ramifiee” at primes over p, a phenomenon which should be related to properties of the corresponding representations of p-adic groups (via a hypotheticallocal Langlands modulo p).
11.00-12.00 Informal discussions (and visit to the CNRS for the participants from England)
12.00-2.00 Lunch at École Normale Supérieure
2.00-3.00 Florian Herzig (IHES)
A Serre-type conjecture for the weights of tame n-dimensional modulo p Galois representations
Abstract: I will discuss the weights in a Serre-type conjecture for n-dimensional mod p Galois representations ρ of the absolute Galois group of Q that are tamely ramified at p. The weight in this context is an irreducible mod p representation of Γ=GLn(Fp). The conjecture predicts the weights in which ρ arises in terms of the reduction mod p of a characteristic 0 representation of Γ associated to ρ restricted to the inertia subgroup at p. It refines, and is more conceptual than, a previous conjecture of Ash, Doud, Pollack, and Sinnott. Some theoretical evidence arising from automorphic representations on GL4 is discussed.
3.00-3.30 Break
3.30-4.30 Toby Gee (Imperial College London)
On crystalline representations and the weights in Serre's conjecture
Abstract : We discuss the relationship between various generalisations of the weight part of Serre's conjecture, crystalline representations, and modularity lifting theorems.

The talks took place in the Amphithéâtre Darboux, Institut Henri Poincaré.

The organizers of the meeting were: Michael Harris (, Guy Henniart (, Marc Hindry (, Ariane Mezard (, Jacques Tilouine (

Second meeting (London, 02/05/2007)
Main page of the London-Paris Number Theory Seminar

This page is maintained by Manuel Breuning. This document was last modified on 2nd April 2009.