Thursday 17 Mar 2016: The integral Bernstein center for GL_n and the local Langlands correspondence in families
David Helm - Imperial College London
The local Langlands correspondence is a relationship between representations of the Galois group of a p-adic field F and the representations of GL_n(F). Objects on both sides of this correspondence naturally vary in algebraic families, and one can therefore ask if it is possible to extend this correspondence to algebraic families of objects. We give an affirmative answer to a reformulation of this question in terms of the Bernstein center, an algebra that acts naturally on a category of representations of GL_n(F).