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Bounds on the Hilbert-Kunz multiplicity

  • Olgur Celikbas (a1), Hailong Dao (a2), Craig Huneke (a3) and Yi Zhang (a4)
Abstract
Abstract

In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[AE] I. M. Aberbach and F. Enescu , Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension, Michigan Math. J. 57 (2008), 116.

[AL] I. M. Aberbach and G. Leuschke , The F-signature and strong F-regularity, Math. Res. Lett. 10 (2003), 5156.

[BE] M. Blickle and F. Enescu , On rings with small Hilbert-Kunz multiplicity, Proc. Amer. Math. Soc. 132 (2004), 25052509.

[ES] F. Enescu and K. Shimomoto , On the upper semi-continuity of the Hilbert-Kunz multiplicity, J. Algebra 285 (2005), 222237.

[HH] M. Hochster and C. Huneke , Tight closure, invariant theory and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31116.

[HL] C. Huneke and G. Leuschke , Two theorems about maximal Cohen-Macaulay modules, Math. Ann. 324 (2002), 391404.

[HMM] C. Huneke , M. A. McDermott , and P. Monsky , Hilbert-Kunz functions for normal rings, Math. Res. Lett. 11 (2004), 539546.

[HY] C. Huneke and Y. Yao , Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular, Proc. Amer. Math. Soc. 130 (2002), 661665.

[Ku] K. Kurano , On Roberts rings, J. Math. Soc. Japan 53 (2001), 333355.

[M] P. Monsky , The Hilbert-Kunz function, Math. Ann. 263 (1983), 4349.

[WY1] K.-i. Watanabe and K.-i. Yoshida , Hilbert-Kunz multiplicity and an inequality between multiplicity and colength, J. Algebra 230 (2000), 295317.

[Y] Y. Yao , Observations on the F-signature of local rings of characteristic p, J. Algebra 299 (2006), 198218.

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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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