The Left Adjoint of Derived Parabolic Induction
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913199152955392 |
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| author | Heyer, Claudius |
| author_facet | Heyer, Claudius |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11581 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Left Adjoint of Derived Parabolic Induction Heyer, Claudius Representation Theory Number Theory 11F85, 18G80, 20G25 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. |
| title | The Left Adjoint of Derived Parabolic Induction |
| topic | Representation Theory Number Theory 11F85, 18G80, 20G25 |
| url | https://arxiv.org/abs/2204.11581 |