Estimates for F-jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers

Abstract

Given an ideal $\mathfrak{a}$ on a smooth variety in characteristic zero, we estimate the $F$-jumping numbers of the reductions of $\mathfrak{a}$ to positive characteristic in terms of the jumping numbers of $\mathfrak{a}$ and the characteristic. We apply one of our estimates to bound the Hartshorne–Speiser–Lyubeznik invariant for the reduction to positive characteristic of a hypersurface singularity.