The multiplier ideal is a universal test ideal

By Karen E. Smith. 2000

90 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/52463b722cfe9df8b99033f7361b2ab1edfac887

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Karl Schwede
2. Manuel Blickle
3. Christopher D. Hacon
4. Irena Swanson
5. Tommaso de Fernex
6. Craig Huneke
7. S. Takagi
8. Wenliang Zhang

In Computational Theory and Mathematics

1. Karl Schwede
2. Manuel Blickle
3. Christopher D. Hacon
4. Tommaso de Fernex
5. Wenliang Zhang
6. Craig Huneke
7. Irena Swanson
8. Nero Budur

In Geometry and Topology

1. Karl Schwede
2. Manuel Blickle
3. Christopher D. Hacon
4. S. Takagi
5. M. Mustaţă
6. Irena Swanson
7. Tommaso de Fernex
8. Craig Huneke

Citations in the corpus

• F-singularities of pairs and Inversion of Adjunction of arbitrary codimension (2003, background): “Hara [8] and Smith [25] independently proved that in a normal Q-Gorenstein ring R of characteristic zero, the multiplier ideal J (R) associated to the unit ideal corresponds to the test ideal τ(R) which plays a central role in the theory of tight closure.”
• F-adjunction (2009, background): “Big test ideals are characteristic p> 0 analogs of multiplier ideals, [Smith 2000; Hara 2001; Takagi 2004b; Hara and Yoshida 2003].”
• On Hodge spectrum and multiplier ideals (2002, background): “tions in algebraic geometry (see [De95], [Si98], [Ei97], [Ka99], [EL99], [ELS01], [CEL01]). Recently, the multiplier ideals turned out to be connected with the test ideals of commutative algebra (see [Sm00], [H01], [Ta02]). For a survey, see [La01], where the algebraic theory of multiplier ideals is”
• Integral closure of ideals, rings, and modules (2006, background): “It has been further studied in Hara [105], [106]; Smith [275]; Takagi [287]; Hara and Takagi [107]; and Hara and Watanabe [109].”
• Singularities on normal varieties (2008, background): “In the (log) Q-Gorenstein setting, multiplier ideals reduce, for sufficiently large characteristics, to the corresponding generalized test ideals (see [ Smi , Har, HY, Tkg]).”
• Discreteness and rationality of F-jumping numbers on singular varieties (2009, background): “all clear from the definition whether discreteness and rationality hold. Likewise, the fact that under reduction modulo p, the multiplier ideal J(X,at) agrees with the test ideal τ(X,at) for p≫ 0 (see [Smi00], [Har01], [HY03], and [Tak04]) does not help with this question since the value of tmay incr”