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

2010/04/02 by Olgur Celikbas, Hailong Dao · 1 citation
Mathematics · #math.AC #msc:13D03

paper · pdf · doi:10.1007/s00209-010-0771-9

published as Math. Z. (2011) 269:1005-1020 (The final publication is available at link.springer.com)

arxiv created 2010/04/02 · arxiv updated 2016/12/16

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_Rⁱ(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_Rⁱ(M,N) needed to ensure that \Ext_Rⁱ(M,N)=0 for all i≫ 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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