发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文通过下降方法对任意基概形上的约化幺半群进行分类，构造了相关结构层并应用于判据、扩张定理及 Vinberg 幺半群的构造。
AI 中文摘要
我们通过从 arXiv:2607.00322 中的分裂分类下降，对任意基概形上的约化幺半群进行分类。对于约化群概形 $G$，我们构造了其基于根系数据层、抽象嘉当环面、抽象外尔群以及外尔锥概形。最后一个概形表示以 $G$ 为单位群的刚性化约化幺半群的同构类函子。作为应用，我们推导出非群幺半群存在性的判据，证明了正规积分基上的扩张定理，并在无拟分裂假设下构造了 Vinberg 幺半群。
英文摘要
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.
Comments19 pages
