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CONTINUITY OF HILBERT–KUNZ MULTIPLICITY AND F-SIGNATURE

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

Published online by Cambridge University Press:  27 December 2018

THOMAS POLSTRA  and
ILYA SMIRNOV Open the ORCID record for ILYA SMIRNOV [Opens in a new window]
THOMAS POLSTRA
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, USA email polstra@math.utah.edu
ILYA SMIRNOV
Affiliation:
Department of Mathematics, Stockholm University, S-106 91, Stockholm, Sweden email smirnov@math.su.se
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Abstract

We establish the continuity of Hilbert–Kunz multiplicity and F-signature as functions from a Cohen–Macaulay local ring $(R,\mathfrak{m},k)$ of prime characteristic to the real numbers at reduced parameter elements with respect to the $\mathfrak{m}$-adic topology.

MSC classification

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure 13H15: Multiplicity theory and related topics 14B05: Singularities

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Type
Article
Information
Nagoya Mathematical Journal , Volume 239 , September 2020 , pp. 322 - 345
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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Footnotes

Polstra was supported in part by NSF Postdoctoral Research Fellowship DMS #1703856.

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