Smooth duality and co-contra correspondence

Abstract

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.

LaTeX 2e with pb-diagram and xy-pic; 64 pages, 16 commutative diagrams; v.4: expanded with many explanations added to make the exposition more accessible to a wider audience; a treatment of admissibility conditions and the involutive triangulated duality added as the second half of the paper; v.5: several misprints corrected, the numbering of sections shifted to agree with the journal version

References in corpus (2)

• Triangulated Matlis equivalence
• Koszulity of cohomology = $K(\pi ,1)$-ness + quasi-formality

Cited by in corpus (6)

• Contramodules
• Abelian right perpendicular subcategories in module categories
• Differential graded Koszul duality: an introductory survey
• The Bernstein center in natural characteristic
• Pseudo-dualizing complexes of bicomodules and pairs of t-structures
• Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors