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arXiv · 1004.0294

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

Olgur Celikbas·Hailong Dao
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Abstract

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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Olgur Celikbas, Hailong Dao. 2010-04-02. Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension. https://doi.org/10.1007/s00209-010-0771-9

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