Algebraic and Arithmetic Geometry Seminar

# Lafforgue variety and $p$-adic representations

## by Kostas I. Psaromiligkos (University of Chicago)

Europe/Rome
Aula Magna (Department of Mathematics)

### Aula Magna

#### Department of Mathematics

Description

We will construct the Lafforgue variety, a parametrizing space for the smooth irreducible representations of a $p$-adic reductive group $G(F)$. Our main tools will be Hecke algebras and a noncommutative version of the Hilbert scheme. The Lafforgue variety comes equipped with a finite projection to the Bernstein variety, which is a bijection outside the locus of a regular function that we call discriminant, generalizing the classical discriminant of algebraic number theory to a non-commutative setting. As an application, we study the irreducibility of induced representations and recover classical results in the case of principal series.