Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T08:05:19.091Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Commutative algebra: Homological methods Local rings and semilocal rings Local theory General commutative ring 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
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© (2020) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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