Banal Characteristic for Reductive p-Adic Groups

Abstract

Let G be a reductive group over a local non-archimedean field F of zero characteristic. For a finite group it is well known that the theory of representations over an algebraically closed field of characteristic which does not divide the order for the group, is the same than over the complex numbers. We prove a similar result for the representations of G. This is far from being trivial (as in the case of a finite group), and not yet known when the characteristic of F is positive. The main ingredient is the existence of discrete subgroups Γ which are cocompact modulo the center.