Abstract
Hara and Yoshida introduced a notion of $\mathfrak{a}$-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.
Citation
Adela Vraciu. "A new version of $\mathfrak{a}$-tight closure." Nagoya Math. J. 192 1 - 25, 2008.
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