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New estimates of Hilbert–Kunz multiplicities for local rings of fixed dimension

Published online by Cambridge University Press:  11 January 2016

Ian M. Aberbach  and
Florian Enescu
Ian M. Aberbach
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA, aberbachi@missouri.edu
Florian Enescu
Affiliation:
Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA, fenescu@gsu.edu
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Abstract

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We present results on the Watanabe–Yoshida conjecture for the Hilbert–Kunz multiplicity of a local ring of positive characteristic. By improving on a “volume estimate” giving a lower bound for Hilbert–Kunz multiplicity, we obtain the conjecture when the ring has either Hilbert–Samuel multiplicity less than or equal to 5 or dimension less than or equal to 6. For nonregular rings with fixed dimension, a new lower bound for the Hilbert–Kunz multiplicity is obtained.

Keywords

13A3513H15
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 212 , December 2013 , pp. 59 - 85
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2013

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