发表机构
Tokyo University of Agriculture and Technology（东京农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含特征零域上有限群作用的Cohen-Macaulay正规环，研究等变非交换平展分解与极大修改代数的导出等价性，证明三维指数2终端奇点的MM模存在性及对应MMA的导出等价。
AI 中文摘要
设S为包含域k的Cohen-Macaulay正规整环，且有限群G作用于S，|G|在k中可逆。我们证明：当G的作用是小作用时，S的G-等变非交换平展分解会诱导出S^G的非交换平展分解。我们还讨论了等变极大修改代数的类似结果。我们引入G-极大修改（G-MM）模的概念，证明S上的G-MM模在某些特殊情形下会诱导出R上的MM模。此外，我们证明三维Q-上Gorenstein Cohen-Macaulay环的Gorenstein MMA是导出等价的。作为这些结果的应用，我们证明了指数为2的三维终端奇点存在MM模，且对应的MMA存在导出等价关系。
英文摘要
Let $S$ be a Cohen-Macaulay normal domain containing a field $k$ with an action of a finite group $G$ with $|G|$ invertible in $k$. We prove that $G$-equivariant noncommutative crepant resolutions of $S$ induce noncommutative crepant resolutions of $S^G$ if the $G$-action is small. We also discuss similar results for equivariant maximal modification algebras. We introduce the notion of $G$-maximal modifying ($G$-MM) module, and we show that $G$-MM module over $S$ induces MM $R$-module in some special cases. Furthermore, we prove that Gorenstein MMAs of three-dimensional $\mathbb{Q}$-Gorenstein Cohen-Macaulay rings are derived equivalent. As an application of these results, we prove the existence of an MM module and derived equivalences of MMAs for three-dimensional terminal singularities of index two.
Comments26 pages
