Duals and admissibility in natural characteristic

Abstract

In this article we introduce a derived smooth duality functor R H o m _ ( − , k ) R\underline {Hom}(-,k) on the unbounded derived category D ( G ) D(G) of smooth k k -representations of a p p -adic Lie group G G . Here k k is a field of characteristic p p . Using this functor we relate various subcategories of admissible complexes in D ( G ) D(G) .