On rings with small Hilbert-Kunz multiplicity
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- by Manuel Blickle and Florian Enescu PDF
- Proc. Amer. Math. Soc. 132 (2004), 2505-2509
Abstract:
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 $p$ and $d$, there exists a number $\epsilon (d,p) > 0$ such that for any nonregular unmixed ring $R$ its Hilbert-Kunz multiplicity is at least $1+\epsilon (d,p)$. We also show that local rings with sufficiently small Hilbert-Kunz multiplicity are Cohen-Macaulay and $F$-rational.References
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Additional Information
- Manuel Blickle
- Affiliation: FB6 Mathematik, Universität Essen, 45117 Essen, Germany
- Email: manuel.blickle@uni-essen.de
- Florian Enescu
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112; Institute of Mathematics of the Romanian Academy, Bucharest, Romania
- Email: enescu@math.utah.edu
- Received by editor(s): October 31, 2002
- Published electronically: April 8, 2004
- Communicated by: Bernd Ulrich
- © Copyright 2004 by the authors
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2505-2509
- MSC (2000): Primary 13A35
- DOI: https://doi.org/10.1090/S0002-9939-04-07469-6
- MathSciNet review: 2054773