Smooth duality in natural characteristic
| Autor: | Jan Kohlhaase |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Pure mathematics Functor General Mathematics 010102 general mathematics Duality (mathematics) Lie group Reductive group 01 natural sciences Tensor product Mathematik 0103 physical sciences Fundamental vector field 010307 mathematical physics 0101 mathematics Mathematics::Representation Theory Smooth structure Vector space Mathematics |
| Zdroj: | Advances in Mathematics. 317:1-49 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2017.06.038 |
| Popis: | We develop a duality theory for admissible smooth representations of p-adic Lie groups on vector spaces over fields of characteristic p. To this end we introduce certain higher smooth duality functors and relate our construction to the Auslander duality of completed group rings. We study the behavior of smooth duality under tensor products, inflation and induction, and discuss the dimension theory of smooth mod-p representations of a p-adic reductive group. Finally, we compute the higher smooth duals of the irreducible smooth representations of GL 2 ( Q p ) in characteristic p and relate our results to the contragredient operation of Colmez. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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