The cohomology of p-adic Deligne-Luszitg schemes of Coxeter type

2024/02/14 by Alexander B. Ivanov, Ivanov, Alexander B., Sian Nie +1
Mathematics · #11G25 #20G05 #20G25 #20G40 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2402.09017

openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the cohomology of the closed Drinfeld stratum of p-Deligne--Lusztig schemes of Coxeter type attached to arbitrary inner forms of unramified groups over a local non-archimedean field. We prove that the corresponding torus weight spaces are supported in exactly one cohomological degree, and are pairwisely non-isomorphic irreducible representations of the pro-unipotent radical of the corresponding parahoric subgroup. We also prove that all Moy--Prasad quotients of this stratum are maximal varieties, and we investigate the relation between the resulting representations and Kirillov's orbit method.

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