%0 Journal Article %T Estimates for F-jumping numbers and bounds for Hartshorne-Speiser-Lyubeznik numbers %A Mircea Mustata %A Wenliang Zhang %J Mathematics %D 2011 %I arXiv %R 10.1215/00277630-2077035 %X Given an ideal J on a smooth variety in characteristic zero, we estimate the F-jumping numbers of the reductions of J to positive characteristic in terms of the jumping numbers of J 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. %U http://arxiv.org/abs/1110.5687v2