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arXiv · 1101.5078

New estimates of Hilbert-Kunz multiplicities for local rings of fixed dimension

Ian M. Aberbach·Florian Enescu
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Abstract

We present results on the Watanabe-Yoshida conjecture for the Hilbert-Kunz multiplicity of a local ring of positive characteristic. By improving on a "volume estimate" giving a lower bound for Hilbert-Kunz multiplicity, we obtain the conjecture when the ring either has Hilbert-Samuel multiplicity less than or equal to five, or dimension less than or equal to six. For non-regular rings with fixed dimension, a new lower bound for the Hilbert-Kunz multiplicity is obtained.

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Ian M. Aberbach, Florian Enescu. 2011-01-26. New estimates of Hilbert-Kunz multiplicities for local rings of fixed dimension. https://doi.org/10.1215/00277630-2335204

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