On rings with small Hilbert-Kunz multiplicity
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
A result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed $p$ (characteristic) and $d$ (dimension), there exist a number $ε(d,p) > 0$ such that any nonregular unmixed ring $R$ has Hilbert-Kunz multiplicity at least $1+ε(d,p)$. We also show that local rings with sufficiently small Hilbert-Kunz multiplicity are Cohen-Macaulay and $F$-rational.
5 pages. to appear in Proc. AMS
5 pages. to appear in Proc. AMS