论文标题
EXT的刚性定理
A Rigidity Theorem for Ext
论文作者
论文摘要
本文的目的是表明，如果$ r $是一个未受到的高度表面，如果$ m $和$ n $有限生成$ r $模块，以及如果$ n \ leq leq \ operatornareameamame {grandatornameamame {m，n）= 0 $，那么$ \ operatorName {ext} _ {r}^{i}（m，n）= 0 $ for $ i \ leq n $。这样的推论说$ \ operatorName {ext} _ {r}^{i}（m，m，m）\ neq 0 $ for $ i \ leq \ leq \ operatoTorname {grange} {m} {m} {m} $和$ m \ m \ neq 0 $。这些结果与Jorgensen的问题和DAO的结果有关。
The goal of this paper is to show that if $R$ is an unramified hypersurface, if $M$ and $N$ are finitely generated $R$ modules, and if $\operatorname{Ext}_{R}^{n}(M,N)=0$ for some $n\leq\operatorname{grade}{M}$, then $\operatorname{Ext}_{R}^{i}(M,N)=0$ for $i\leq n$. A corollary of this says that $\operatorname{Ext}_{R}^{i}(M,M)\neq 0$ for $i\leq\operatorname{grade}{M}$ and $M\neq 0$. These results are related to a question of Jorgensen and results of Dao.
