  The aim of this paper is to explain how to get a complex of smooth
representations out of the dual vector space to a smooth representation of a
p-adic Lie group, in natural characteristic. The construction does not depend
on any finiteness/admissibility assumptions. Imposing such an assumption, one
obtains an involutive duality on the derived category of complexes of smooth
modules with admissible cohomology modules. The paper can serve as an
introduction to the results about representations of locally profinite groups
contained in the author's monograph on semi-infinite homological algebra
arXiv:0708.3398.
