A characterization of multiplier ideals via ultraproducts

2022/06/17 by Yamaguchi, Tatsuki · 1 citation
#13H10 #14B05 #14F18 #14M05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.08668

Abstract

In this paper, using ultra-Frobenii, we introduce a variant of Schoutens' non-standard tight closure, ultra-tight closure, on ideals of a local domain R essentially of finite type over ℂ. We prove that the ultra-test ideal τ_{\rm u}(R,\mathfraka^t), the annihilator ideal of all ultra-tight closure relations of R, coincides with the multiplier ideal J(Spec R,\mathfraka^t) if R is normal ℚ-Gorenstein. As an application, we study a behavior of multiplier ideals under pure ring extensions.

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