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<p>If a module <i>M</i> has finite projective dimension, then the Ext modules of <i>M</i> against any other module eventually vanish and the projective dimension of <i>M</i> gives a uniform bound for this vanishing. For modules of infinite projective dimension, there can still exist a bound. Such a bound is called the Auslander bound. In this paper, we define a similar bound for complexes and give applications.</p>

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The Auslander bound for complexes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月22日

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  • Andrew J. Soto Levins

摘要

If a module M has finite projective dimension, then the Ext modules of M against any other module eventually vanish and the projective dimension of M gives a uniform bound for this vanishing. For modules of infinite projective dimension, there can still exist a bound. Such a bound is called the Auslander bound. In this paper, we define a similar bound for complexes and give applications.