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arXiv · 2203.15133

Centralizers of sections of a reductive group scheme

Sean Cotner
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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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Sean Cotner. 2022-03-28. Centralizers of sections of a reductive group scheme. https://arxiv.org/abs/2203.15133

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