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ERRATUM: CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE

Part of: General commutative ring theory Local rings and semilocal rings Commutative algebra: Homological methods Local theory

Published online by Cambridge University Press:  23 October 2020

THOMAS POLSTRA  and
ILYA SMIRNOV
THOMAS POLSTRA
Affiliation:
Department of Mathematics University of UtahSalt Lake City, UtahUSApolstra@math.utah.edu
ILYA SMIRNOV*
Affiliation:
Department of Mathematics Stockholm UniversitySE - 106 91StockholmSweden
*
smirnov@math.su.se
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Abstract

Unfortunately, there is a mistake in [PS, Lemma 3.10] which invalidates [PS, Theorem 3.12]. We show that the theorem still holds if the ring is assumed to be Gorenstein.

MSC classification

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Secondary: 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure 13H15: Multiplicity theory and related topics 14B05: Singularities
Type
Correction
Information
Nagoya Mathematical Journal , Volume 245 , March 2022 , pp. 229 - 231
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Copyright
© (2020) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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References

De Stefani, A. and Smirnov, I., Stability and deformation of F-singularities, preprint, 2020. https://arxiv.org/abs/2002.00242.Google Scholar
Gabber, O. and Orgogozo, F., Sur la p-dimension des corps , Invent. Math. 174 (2008), 47–80.CrossRefGoogle Scholar
Huneke, C. and Leuschke, G. J., Two theorems about maximal Cohen-Macaulay modules , Math. Ann. 324 (2002), 391–404.CrossRefGoogle Scholar
Kunz, E., On Noetherian rings of characteristic p , Amer. J. Math. 98 (1976), 999–1013.CrossRefGoogle Scholar
Polstra, T. and Smirnov, I., Continuity of Hilbert–Kunz multiplicity and F-signature, Nagoya Math. J., 239:322–345, 2020.CrossRefGoogle Scholar
Polstra, T. and Tucker, K., F-signature and Hilbert-Kunz multiplicity: A combined approach and comparison , Algebra Number Theory 12 (2018), 61–97.CrossRefGoogle Scholar