Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Details Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

2010-04-02

arxiv.org/abs/1004.0294v1

Mathematics

Commutative Algebra

Scientific paper

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.

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