2004/03/29 by Peter Schneider, Schneider, Peter, Jeremy Teitelbaum +1
Mathematics · #11S80 #22E50 #Advanced Algebra and Geometry #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #math.NT #math.RT #msc:11S80 #msc:22E50
paper · pdf · doi:10.48550/arxiv.math/0403498
36 pages, uses xypic
openalex publication_date 2004/03/29 · arxiv created 2004/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of a p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an involutive "duality" functor from the bounded derived category of modules over the distribution algebra of G with coadmissible cohomology to itself. On the subcategory corresponding to complexes of smooth representations, this functor induces the usual smooth contragredient (with a degree shift). Although we construct our functor in general we obtain its involutivity, for technical reasons, only in the case of locally Qp-analytic groups.