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

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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 \({{\rm {Ext}}_R^i(M,N)}\) which generalizes Buchweitz’s notion of the Herbrand difference. We exploit this pairing to examine the number of consecutive vanishing of \({{\rm {Ext}}_R^i(M,N)}\) needed to ensure that \({{\rm {Ext}}_R^i(M,N)=0}\) 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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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska–Lincoln, 311 Avery Hall, Lincoln, NE, 68588–0323, USA

    Olgur Celikbas

  2. Department of Mathematics, University of Kansas, 405 Snow Hall, 1460 Jayhawk Blvd, Lawrence, KS, 66045-7523, USA

    Hailong Dao

Authors
  1. Olgur Celikbas
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  2. Hailong Dao
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Correspondence to Hailong Dao.

Additional information

H. Dao is partially supported by NSF grant DMS 0834050.

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Celikbas, O., Dao, H. Asymptotic behavior of Ext functors for modules of finite complete intersection dimension. Math. Z. 269, 1005–1020 (2011). https://doi.org/10.1007/s00209-010-0771-9

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  • DOI: https://doi.org/10.1007/s00209-010-0771-9

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