Duality for admissible locally analytic representations

By P. Schneider, Jeremy Teitelbaum. 2004

54 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c61ddb1ee94eac63003589d95141694165fc51ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. S. Wadsley
2. K. Ardakov
3. Jan Kohlhaase
4. Vytautas Paškūnas
5. O. Ben-Bassat
6. Kobi Kremnizer

In Mathematical Physics

1. S. Wadsley
2. K. Ardakov
3. Jan Kohlhaase
4. Vytautas Paškūnas
5. O. Ben-Bassat
6. Kobi Kremnizer

Citations in the corpus

• On irreducible representations of compact $p$-adic analytic groups (2011, background): “In a series of papers including [68, 69, 70, 71] Schneider and Teitelbaum study a class of rings that they call the distribution algebras D(G,K) of a p-adic analytic group G.”
• The cohomology of locally analytic representations (2010, methodology): “Thus, w 1 2 satisfies assumption (FIN) of [37], section 6, and the arguments of [37], Lemma 6.”