A new version of $\mathfrak{a}$-tight closure

Details A new version of $\mathfrak{a}$-tight closure A new version of $\mathfrak{a}$-tight closure

2007-03-30

arxiv.org/abs/math/0703932v1

Mathematics

Commutative Algebra

22 pages

Scientific paper

Hara and Yoshida introduced a notion of $\aaa$-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.

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