Types et inductions pour les représentations modulaires des groupes p-adiques

Abstract

Bushnell-Kutzko's theory of types aims at describing the category of smooth complex representations of a p-adic group, relying on the “classical” theory by Casselman, Bernstein, etc. Here we are interested in modular representations of a p-adic group, i.e. representations with coefficients in a field of characteristic different from p. Several proofs of “classical” results in the complex case are no longer valid, but we intend here to use the theory of types —as well the axiomatization of [BK1] as the concrete cases of [Vig2]— in order to adapt some of these results to the modular situation. In particular, some finiteness results are obtained for GL( N) in the appendix by M.-F. Vignéras.