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arXiv · 0708.0537

Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension

Ian M. Aberbach·Florian Enescu
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Abstract

Let $(R,\m)$ be a formally unmixed local ring of positive prime characteristic and dimension $d$. We examine the implications of having small Hilbert-Kunz multiplicity (i.e., close to 1). In particular, we show that if $R$ is not regular, there exists a lower bound, strictly greater than one, depending only on $d$, for its Hilbert-Kunz multiplicity.

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Ian M. Aberbach, Florian Enescu. 2008-04-04. Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension. https://arxiv.org/abs/0708.0537

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