Discreteness and rationality of $F$-jumping numbers on singular varieties

Abstract

We prove that the $F$-jumping numbers of the test ideal $τ(X; Δ, \ba^t)$ are discrete and rational under the assumptions that $X$ is a normal and $F$-finite variety over a field of positive characteristic $p$, $K_X+\Delta$ is $\bQ$-Cartier of index not divisible $p$, and either $X$ is essentially of finite type over a field or the sheaf of ideals $\ba$ 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.

29 pages, minor changes, to appear in Mathematische Annalen

References in corpus (2)

• Singularities on normal varieties
• Centers of F-purity

Cited by in corpus (10)

• On the behavior of test ideals under finite morphisms
• Test ideals of non-principal ideals: Computations, Jumping Numbers, Alterations and Division Theorems
• On Strongly $F$-Regular Inversion of Adjunction
• Test ideals in rings with finitely generated anti-canonical algebras
• Discrepancies of non-$\Q$-Gorenstein varieties
• Comparing multiplier ideals to test ideals on numerically Q-Gorenstein varieties
• Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ
• The TestIdeals package for Macaulay2
• Discreteness of $F$-jumping numbers at isolated non-Q-Gorenstein points
• Limit $F$-signature functions of two-variable binomial hypersurfaces