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arXiv · 2507.22364

On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring

Van Duc Trung
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Abstract

Let $(R,\mathfrak{m})$ be a Noetherian local ring, and let $J$ be an arbitrary ideal of $R$. Suppose $M$ is a finitely generated $R$-module. Let $x_1,\ldots,x_r$ be a $J$-filter regular sequence on $M$. We provide an explicit number $N$ such that the Bass and Betti numbers of $M/(x_1, \ldots, x_r)M$ are preserved when we perturb the sequence $x_1, \ldots,x_r$ by $\varepsilon_1, \ldots, \varepsilon_r \in \mathfrak{m}^N$.

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Van Duc Trung. 2025-07-30. On the Stability of Bass and Betti Numbers under Ideal Perturbations in a Local Ring. https://arxiv.org/abs/2507.22364

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