Publication date:
7 September 2017
Source:Advances in Mathematics, Volume 317
Author(s): Jan Kohlhaase
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 ${\mathrm{GL}}_2({\mathbb{Q}}_p)$ in characteristic p and relate our results to the contragredient operation of Colmez.