2007/03/30 by Adela Vraciu, Vraciu, Adela
Mathematics · #13A35 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A35
paper · pdf · doi:10.48550/arxiv.math/0703932
22 pages
arxiv created 2007/03/30 · arxiv updated 2009/12/01
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.