有限完全交维数模的Ext函子的渐近性
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
摘要：
设$R$是局部环，$M$和$N$是局部生成的$R$ -模，使得$M$有有限的完全交维数.在本文中，我们定义和研究，在一定的条件下，一对使用模块$\Ext_R^i(M,N)$推广Buchweitz的概念的Herbrand差异。我们利用这种配对来检查$\Ext_R^i(M,N)$连续消失的数量，以确保所有$i\gg 0$的$\Ext_R^i(M,N)=0$。我们的结果恢复和改进的文献中的大多数已知的界限，特别是当$R$的维数最多为2。
英文摘要：
Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules $\Ext_R^i(M,N)$ which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of $\Ext_R^i(M,N)$ needed to ensure that $\Ext_R^i(M,N)=0$ for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
