p-Adic Representations

September 12 – 16, 2005
Centre de recherches mathématiques

Organizers: Adrian Iovita (Concordia) et Henri Darmon (McGill)

The main topics to be adressed in this workshop are related to a p-adic Langlands correspondence and its relationship to p-adic families of motives. More precisely the p-adic Langlands correspondence is a correspondence between p-adic Galois representations of dimension n (of the absolute Galois group of Q_p) and certain representations of GL_n(Q_p) on p-adic topological vector spaces. So far this correspondence has been worked out for n=1 and in certain cases for n=2.

The case n=2 is most interesting. Representations of GL_2(Q_p) have been associated to semi-stable Galois representations and more recently even to representations which do not come from algebraic geometry (the so called "représentations triangulines"). In particular, as the representations attached to overconvergent modular forms (which are constituents of p-adic families of Galois represntations) are trianguline, one may wonder if there exist p-adic families of GL_2(Q_p) representations on p-adic spaces and if the local Langlands correspondence is compatible with the p-adic families on the two sides.