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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2508.14598 |
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| _version_ | 1866908496316858368 |
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| author | Hoff, Manuel Meier, Sarah Diana Spieß, Michael Heyer, Claudius |
| author_facet | Hoff, Manuel Meier, Sarah Diana Spieß, Michael Heyer, Claudius |
| contents | We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor $\operatorname{Ord}_P^G$. This functor plays an important role in the theory of mod $p$ representations of $p$-adic reductive groups. A key ingredient for our proof is a comparison between certain small and parabolic inductions. Additionally, our method yields an explicit description of Vignéras' right adjoint to parabolic induction.
In the appendix (joint with Heyer) we apply our results to obtain a mod $p$ variant of Bernstein's Second Adjointness, i.e. we show that the right and left adjoint of derived parabolic induction are isomorphic (on complexes with admissible cohomology) up to a cohomological shift and twist by a character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14598 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Right Derived Functors of Ordinary Parts Hoff, Manuel Meier, Sarah Diana Spieß, Michael Heyer, Claudius Representation Theory Number Theory We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor $\operatorname{Ord}_P^G$. This functor plays an important role in the theory of mod $p$ representations of $p$-adic reductive groups. A key ingredient for our proof is a comparison between certain small and parabolic inductions. Additionally, our method yields an explicit description of Vignéras' right adjoint to parabolic induction. In the appendix (joint with Heyer) we apply our results to obtain a mod $p$ variant of Bernstein's Second Adjointness, i.e. we show that the right and left adjoint of derived parabolic induction are isomorphic (on complexes with admissible cohomology) up to a cohomological shift and twist by a character. |
| title | On the Right Derived Functors of Ordinary Parts |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2508.14598 |