Centralizers of sections of a reductive group scheme
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.
- Pub Date:
- March 2022
- Mathematics - Algebraic Geometry;
- Primary 20G35;
- Secondary 14L15;
- 33 pages. Split from the previous version into this and arXiv:2211.08383. Comments welcome!