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Upper semi-continuity of the Hilbert–Kunz multiplicity

Part of: General commutative ring theory Commutative algebra: Homological methods Arithmetic rings and other special rings

Published online by Cambridge University Press:  02 February 2016

Ilya Smirnov
Ilya Smirnov*
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA email ismirnov@umich.edu Current address: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA
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Abstract

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We prove that the Hilbert–Kunz multiplicity is upper semi-continuous in F-finite rings and algebras of essentially finite type over an excellent local ring.

Keywords

Hilbert–Kunz multiplicitysemi-continuityF-finite rings

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 13F40: Excellent rings
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 3 , March 2016 , pp. 477 - 488
Copyright
© The Author 2016 

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