The Left Adjoint of Derived Parabolic Induction
| Autor: | Heyer, Claudius |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Math. Z., volume 305, number 46, 2023, 60 pages |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00209-023-03385-5 |
| Popis: | We prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod $p$ representations of a $p$-adic reductive group, admits a left adjoint $\mathrm{L}(U,-)$. We study the cohomology functors $\mathrm{H}^i\circ \mathrm{L}(U,-)$ in some detail and deduce that $\mathrm{L}(U,-)$ preserves bounded complexes and global admissibility in the sense of Schneider--Sorensen. Using $\mathrm{L}(U,-)$ we define a derived Satake homomorphism und prove that it encodes the mod $p$ Satake homomorphisms defined explicitly by Herzig. Comment: 52 pages. Comments welcome! v2: Strengthened Corollary 3.4.20 and removed the now obsolete construction of a character; v3: several other small changes. This version may differ slightly from published version |
| Databáze: | arXiv |
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