Perfecting group schemes

Fuente: arXiv
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Main Authors: Coulembier, Kevin, Williamson, Geordie
Format: Preprint
Published: 2022
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author Coulembier, Kevin
Williamson, Geordie
author_facet Coulembier, Kevin
Williamson, Geordie
contents We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a bijection with the set of classifying spaces of compact connected Lie groups topologically localised away from the characteristic. We also study the representations of perfectly reductive groups. We establish a highest weight classification of simple modules, the decomposition into blocks, and relate extension groups to those of the underlying abstract group.
format Preprint
id arxiv_https___arxiv_org_abs_2206_05867
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Perfecting group schemes
Coulembier, Kevin
Williamson, Geordie
Representation Theory
Algebraic Geometry
Group Theory
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a bijection with the set of classifying spaces of compact connected Lie groups topologically localised away from the characteristic. We also study the representations of perfectly reductive groups. We establish a highest weight classification of simple modules, the decomposition into blocks, and relate extension groups to those of the underlying abstract group.
title Perfecting group schemes
topic Representation Theory
Algebraic Geometry
Group Theory
url https://arxiv.org/abs/2206.05867