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

Ian M. Aberbach; Florian Enescu

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

Commutative Algebra 2008-04-07 v2

Authors: Ian M. Aberbach , Florian Enescu

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.

Keywords

Hilbert-Kunz multiplicity local rings positive prime characteristic regular ring lower bounds formally unmixed

Cite

@article{arxiv.0708.0537,
  title  = {Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension},
  author = {Ian M. Aberbach and Florian Enescu},
  journal= {arXiv preprint arXiv:0708.0537},
  year   = {2008}
}

Comments

14 pages, to appear in Michigan Math Journal; a number of corrections were performed according to the referee's comments, including a weakening of Corollary 3.10 which led to a small change in the lower bound in Theorem 4.12

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

Abstract

Keywords

Cite

Comments

Related papers