On the Right Derived Functors of Ordinary Parts

2025/08/20 by Manuel Hoff, Sarah Diana Meier, Hoff, Manuel +5
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2508.14598

openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor 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.

Citations

• 6-Functor Formalisms and Smooth Representations
• The Geometrical Lemma for Smooth Representations in Natural Characteristic
• Finiteness for Hecke algebras of p-adic groups
• Modulo p representations of reductive p-adic groups: functorial properties
• Comparison of compact induction with parabolic induction

Related

• The Geometrical Lemma for Smooth Representations in Natural Characteristic
• The Second Adjointness Theorem for reductive p-adic groups
• Towards the Derived Jacquet-Emerton Module Functor
• Modulo p representations of reductive p-adic groups: functorial properties
• Parabolic induction and the Harish-Chandra D-module