Joel Bellaiche

Unitary eigenvarieties and families of Galois representations

In this introductory talk, we will define the eigenvarities attached to unitary groups. We will explain that they carry a family of Galois representations, or more precisely a Galois pseudorepresentations (a.k.a pseudocharacter). After a short introduction to the general theory of pseudocharacter, we will explain how the reducibility locus of the pseudocharacter carried by an eigenvariety can often be controlled. (Based on a joint work with G. Chenevier)