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arXiv · 2310.11697

Asymptotic behavior of homological invariants of localizations of modules

Kaito Kimura
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Abstract

Let $R$ be a commutative noetherian ring, $I$ an ideal of $R$, and $M$ a finitely generated $R$-module. We consider the asymptotic injective dimensions, projective dimensions, Bass numbers, and Betti numbers of localizations of $M/I^n M$ at prime ideals of $R$ and prove that these invariants are stable or have polynomial growth for large integers $n$ that do not depend on the prime ideals.

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Kaito Kimura. 2023-10-18. Asymptotic behavior of homological invariants of localizations of modules. https://arxiv.org/abs/2310.11697

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