Abstract
Let F be a nite extension of Qp. We associate, to certain smooth p-modular representations \pi of GL2(F), a module S(\pi) on the mod p Iwasawa of the standard Iwahori subgroup I of GL2(F). When F is unrami ed, we obtain a module on a suitable formally smooth Fq-algebra, endowed with an action of O_F (the units in the ring of integers of F) and an O_F F equivariant, Frobenius semilinear endomorphism which turns out to be p-etale. We study the torsion properties of such module, as well as its Iwahori-radical ltration.