P-module representations of p-adic reductive groups

Considering congruences of classical modular forms naturally leads to the investigation of smooth representations of GL(2, Q(p)) on vector spaces over a field of positive characteristic. The case where that characteristic is p is very peculiar and its study started only recently. We deal here with a general reductive group over a non-Archimedean local field F of residue characteristic p, and study its smooth representations over a field of characteristic p. We develop the first stages of a general theory, and prove in particular that a quotient of an admissible representation is still admissible, provided F has characteristic 0.