Centralizers of sections of a reductive group scheme

2022/03/28 by Sean Cotner, Cotner, Sean
Chemistry · Mathematics · #20G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Axial and Atropisomeric Chirality Synthesis #FOS: Mathematics #Primary 20G35 #Secondary 14L15

paper · pdf · doi:10.48550/arxiv.2203.15133

openalex publication_date 2022/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper proves a number of flatness results for centralizers of sections of a reductive group scheme over a general base scheme. To this end, we establish relative versions of the Jordan decomposition. Using our results, we obtain a canonical flattening stratification for the universal centralizer of a simply connected semisimple group scheme over a base of good characteristic. We also investigate the structure of centralizers and conjugacy classes of unipotent and nilpotent sections over general bases.

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