PreprintCC BY-NC-ND 4.0arXiv
Classification of reductive monoids
Abstract
We classify reductive monoids over arbitrary base schemes by descent from the split classification in arXiv:2607.00322. For a reductive group scheme G, we construct its sheaf of based root data, abstract Cartan torus, abstract Weyl group, and a scheme of Weyl cones. The last of these represents the functor of isomorphism classes of rigidified reductive monoids with unit group G. As applications, we deduce a criterion for the existence of monoids that are not groups, prove an extension theorem over normal integral bases, and construct the Vinberg monoids without a quasi-split hypothesis.
Related
- Quantized integral models of reductive monoids
- Reductive monoids over general base
- Presentation of monoids generated by a projection and an involution
- A Categorical Realization of the (2-)Category of Monoids via Sch{ü}tzenberger Categories and Strict Factorization Systems
- Generation of Iterated Wreath Products Constructed from Full Transformation Monoids and Symmetric Groups
BibTeX
@misc{chi2026classification,
title = {{Classification of reductive monoids}},
author = {Jingren Chi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05847},
eprint = {2610.05847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05847},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Classification of reductive monoids
AU - Jingren Chi
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05847
UR - https://arxiv.org/abs/2610.05847
AB - We classify reductive monoids over arbitrary base schemes by descent from the split classification in arXiv:2607.00322. For a reductive group scheme G, we construct its sheaf of based root data, abstract Cartan torus, abstract Weyl group, and a scheme of Weyl cones. The last of these represents the functor of isomorphism classes of rigidified reductive monoids with unit group G. As applications, we deduce a criterion for the existence of monoids that are not groups, prove an extension theorem over normal integral bases, and construct the Vinberg monoids without a quasi-split hypothesis.
ER -