Discreteness and rationality of F-jumping numbers on singular varieties

By Manuel Blickle, Karl Schwede, S. Takagi, Wenliang Zhang. 2009

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We prove that the F-jumping numbers of the test ideal $${\tau(X; \Delta, \mathfrak{a}^t)}$$ are discrete and rational under the assumptions that X is a normal and F-finite scheme over a field of positive characteristic p, KX + Δ is $${\mathbb {Q}}$$-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals $${\mathfrak{a}}$$ is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero.

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

View Paper: https://www.semanticscholar.org/paper/9340be6023a2ad887cc55f6927a940e11e82ff1c

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In Algebra and Number Theory

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Citations in the corpus

IMPANGA lecture notes on log canonical thresholds (2011, background): “om [BMS2] gives the analogue for the rationality and the discreteness of the jumping numbers of the multiplier ideals of a given ideal. For extensions to various other settings, see [BMS1], [KLZ] and [BSTZ]. Theorem 2.17. If ais a nonzero ideal in R, then the set of F-jumping numbers of ais a discre”
Ordinary varieties and the comparison between multiplier ideals and test ideals (2010, background): “he results on the jumping numbers for the test ideals, we mention them because of the analogy with the case of multiplier ideals. For the proofs, see [BMS] for the case when Y is smooth and D= 0, and [BSTZ] for the general case. Given any (Y,D,a) as above, and any λ≥ 0, there is ε>0 such that τ(Y”
p −1-Linear Maps in Algebra and Geometry (2012, result): “s natural to expect that the set of jumping numbers for the test ideal is discrete. In the case that Xis smooth this was shown to be the case in [BMS08] and [BMS09]. The singular case was obtained in [BSTZ10], see also [Har06, KLZ09, ST08, TT08, STZ12, AMBZ12` ]. We will outline here an elementary p”