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

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

2007-08-03

arxiv.org/abs/0708.0537v2

Mathematics

Commutative Algebra

14 pages, to appear in Michigan Math Journal; a number of corrections were performed according to the referee's comments, incl

Scientific paper

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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