Springer isomorphisms over a general base scheme
Algebraic Geometry
2022-11-16 v1 Number Theory
Representation Theory
Abstract
We establish the existence of Springer isomorphisms for reductive group schemes over general base schemes. For this, we first study centralizers of fiberwise regular sections of reductive group schemes, and we establish their flatness in many cases. At the end, we give several arguments to show that the hypotheses in our results are essentially optimal. Our results clarify some aspects of Springer isomorphisms even over a field, and the arguments simplify considerably in this case.
Cite
@article{arxiv.2211.08383,
title = {Springer isomorphisms over a general base scheme},
author = {Sean Cotner},
journal= {arXiv preprint arXiv:2211.08383},
year = {2022}
}
Comments
50 pages. This is an expansion of part of arXiv:2203.15133v1. Comments welcome!