Lafforgue variety and $p$-adic representations – Kostas I. Psaromiligkos (University of Chicago)


Department of Mathematics, Aula Magna.


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.

Further information is available on the event page on the Indico platform.

Torna in cima