Given an ideal on a smooth variety in characteristic zero, we estimate the -jumping numbers of the reductions of to positive characteristic in terms of the jumping numbers of 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.
"Estimates for -jumping numbers and bounds for Hartshorne–Speiser–Lyubeznik numbers." Nagoya Math. J. 210 133 - 160, June 2013. https://doi.org/10.1215/00277630-2077035