Smooth duality in natural characteristic

We develop a duality theory for admissible smooth representations of p-adic Lie groups on vector spaces over fields of characteristic p. To this end we introduce certain higher smooth duality functors and relate our construction to the Auslander duality of completed group rings. We study the behavior of smooth duality under tensor products, inflation and induction, and discuss the dimension theory of smooth mod-p representations of a p-adic reductive group. Finally, we compute the higher smooth duals of the irreducible smooth representations of GL(2)(Q(p)) in characteristic p and relate our results to the contragredient operation of Colmez. (C) 2017 Elsevier Inc. All rights reserved.