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October 7, 2025Open Access

Ext functors, support varieties and Hilbert polynomials over complete intersection rings

Key Points

The study shows that for all large indices, the polynomial type function stabilizes as a constant.
Invariant values defined by the $r_0^I(M)$ and $r_1^I(M)$ are crucial for understanding module properties.
If $r^I(M)$ is non-positive, a bound exists for the regularity of the components of $G_I( ext{Ω}^i(M))$.
Applications to the syzgetic Artin-Rees property of modules illustrate the significance of these findings.

Abstract

Let (A, m) be a complete intersection of dimension d 1 and codimension c 1. Let I be an m-primary ideal and let M be a finitely generated A-module. For i 1 let ᵢI (M) be the degree of the polynomial type function n (ExtⁱA (M, A/Iⁿ) ). We show that for j = 0, 1 and for all i 0 we have ₂₈ +₉I (M) is a constant and let r₀I (M) and r₁I (M) denote these constant values. Set rI (M) = \ r₀I (M), r₁I (M) \. We show that rI (M) is an invariant of I, A and the support variety of M. We set the degree of the zero polynomial to be -. If rI (M) 0 then we show that reg \ GI (ⁱ (M) ) for i 0 is bounded. We give an application of this result to syzgetic Artin-Rees property of M. We also give several examples which illustrate our results.

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Cite This Study

Tony J. Puthenpurakal (Sun,) studied this question.

synapsesocial.com/papers/68e5a0557f330f793683f33b https://doi.org/https://doi.org/10.48550/arxiv.2502.16494

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