标题： 局部唯一因子分解域上Ext模的消失性 显示英文标题

标题： On the vanishing of Ext modules over a local unique factorization domain with an isolated singularity

摘要： 本文提供了一种方法，从给定的诺特完备等特征局部环中得到一个具有孤立奇点的诺特等特征局部唯一因子分解整环，并保持某些性质。 这被应用于研究Ext模的（非）消没性。 证明了存在一个具有孤立奇点的Gorenstein局部UFD$A$，使得$\operatorname{Ext}_A^{\gg0}(M,N)=0$不蕴含$\operatorname{Ext}_A^{\gg0}(N,M)=0$，一个具有孤立奇点的Gorenstein局部UFD$B$，使得$\operatorname{Tor}_{>0}^B(M,N)=0$不蕴含$\operatorname{depth}(M\otimes_B N)=\operatorname{depth} M+\operatorname{depth} N-\operatorname{depth} B$，并且一个具有孤立奇点的Cohen-Macaulay局部UFD$C$，使得$\operatorname{Ext}_C^{>0}(M,C)=0$不蕴含$M$的完全可缩性。 显示英文摘要

摘要： This paper provides a method to get a noetherian equicharacteristic local UFD with an isolated singularity from a given noetherian complete equicharacteristic local ring, preserving certain properties. This is applied to invesitgate the (non)vanishing of Ext modules. It is proved that there exist a Gorenstein local UFD $A$ having an isolated singularity such that $\operatorname{Ext}_A^{\gg0}(M,N)=0$ does not imply $\operatorname{Ext}_A^{\gg0}(N,M)=0$, a Gorenstein local UFD $B$ having an isolated singularity such that $\operatorname{Tor}_{>0}^B(M,N)=0$ does not imply $\operatorname{depth}(M\otimes_B N)=\operatorname{depth} M+\operatorname{depth} N-\operatorname{depth} B$, and a Cohen-Macaulay local UFD $C$ having an isolated singularity such that $\operatorname{Ext}_C^{>0}(M,C)=0$ does not imply the total reflexivity of $M$.