Duality for admissible locally analytic representations

Details Duality for admissible locally analytic representations Duality for admissible locally analytic representations

2004-03-29

arxiv.org/abs/math/0403498v2

Mathematics

Number Theory

36 pages, uses xypic

Scientific paper

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.

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