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PreprintCC BY-NC-ND 4.0arXiv

Reductive monoids over general base

  • Jingren Chi
  • Simon Jacques
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Abstract

We develop a theory of affine algebraic monoids over connected base schemes whose unit groups are split reductive groups. Our main result is a classification theorem for such objects, generalizing the work of Vinberg and Rittatore over a field. As applications, we obtain combinatorial descriptions and normality properties of orbit closures, prove a Steinberg-type theorem on adjoint quotients of split reductive monoids, and construct finite type integral models of the Vinberg monoids.

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Cite

BibTeXRIS
BibTeX
@misc{chi2026reductive,
  title = {{Reductive monoids over general base}},
  author = {Jingren Chi and Simon Jacques},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.00322},
  eprint = {2607.00322},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.00322},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Reductive monoids over general base
AU  - Jingren Chi
AU  - Simon Jacques
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.00322
UR  - https://arxiv.org/abs/2607.00322
AB  - We develop a theory of affine algebraic monoids over connected base schemes whose unit groups are split reductive groups. Our main result is a classification theorem for such objects, generalizing the work of Vinberg and Rittatore over a field. As applications, we obtain combinatorial descriptions and normality properties of orbit closures, prove a Steinberg-type theorem on adjoint quotients of split reductive monoids, and construct finite type integral models of the Vinberg monoids.
ER  -