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arXiv · 2511.12946

Improved Bounds for the s-multiplicity

Zhongkui Liu·Junquan Qin·Xiaoyan Yang
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Abstract

Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same residue eld k and prime characteristic p > 0. We establish some formulas relating the h-function and s-multiplicity of the ber product R T S in terms of the h-functions and s-multiplicities of R, T and S. Furthermore, we derive formulas that connect the h-function and s-multiplicity of the idealization ring R M to the corresponding invariants of R and M, where M is a nitely generated R-module. As applications of these results, we derive new estimates for the Taylor-Miller question and the Watanabe-Yoshida conjecture concerning s-multiplicity.

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Zhongkui Liu, Junquan Qin, Xiaoyan Yang. 2025-11-17. Improved Bounds for the s-multiplicity. https://arxiv.org/abs/2511.12946

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