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A New Version of α-Tight Closure

Published online by Cambridge University Press:  11 January 2016

Adela Vraciu
Adela Vraciu*
Affiliation:
Department of Mathematics University of South Carolina, Columbia SC 29205, U.S.A., vraciu@math.sc.edu
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Abstract

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Hara and Yoshida introduced a notion of α-tight closure in 2003, and they proved that the test ideals given by this operation correspond to multiplier ideals. However, their operation is not a true closure. The alternative operation introduced here is a true closure. Moreover, we define a joint Hilbert-Kunz multiplicity that can be used to test for membership in this closure. We study the connections between the Hara-Yoshida operation and the one introduced here, primarily from the point of view of test ideals. We also consider variants with positive real exponents.

Keywords

13A35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 192 , 2008 , pp. 1 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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