The Geometrical Lemma for Smooth Representations in Natural Characteristic — Claudius Heyer (Universität Münster)Séminaire « Arithmétique »
In the theory of smooth representations of a p-adic reductive group, the Geometrical Lemma, due to Bernstein–Zelevinsky and Casselman, describes parabolic restrictions of parabolically induced representations by providing a filtration whose graded pieces can be described explicitly. Classically, the Geometrical Lemma works well whenever the coefficient field has characteristic different from p, but for mod p representations the filtration degenerates to a single degree. As it turns out, this defect can be resolved by working on the level of derived categories: the missing graded pieces appear in various cohomological degrees, which are therefore invisible on the abelian level. In this talk I will present the derived version of the Geometrical Lemma and, if time permits, describe some applications.