Types and inductions for modular representations of p-adic groups

Bushnell-Kutzko's theory of types aims at describing the category of smooth complex representations of a p-adic group, relying on the "classical" theo ry by Casselman, Bernstein, etc. Here we are interested in modular represen tations of a p-adic group, i.e. representations with coefficients in a fiel d of characteristic different from p. Several proofs of "classical" results in the complex case are no longer valid, but we intend here to use the the ory of types -as well the axiomatization of [BK1] as the concrete cases of [Vig2]- in order to adapt some of these results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. I n particular, some finiteness results are obtained for GL(N) in the appendi x by M.-F. Vigneras. (C) Elsevier, Paris.