Bounds on the Hilbert-Kunz Multiplicity

Abstract

In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed non-regular local rings, bounding them uniformly away from one. Our results improve previous work of Aberbach and Enescu.

Some minor typos fixed, especially Theorem 3.7 (min instead of max). Corollary 2.4 is added by the referee's suggestion