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

TL;DR

This paper provides estimates for F-jumping numbers of ideal reductions from characteristic zero to positive characteristic and applies these estimates to bound the Hartshorne-Speiser-Lyubeznik invariant for hypersurface singularities.

Contribution

It introduces new bounds relating F-jumping numbers and characteristic, and applies these to estimate the Hartshorne-Speiser-Lyubeznik invariant.

Findings

Derived bounds for F-jumping numbers in positive characteristic

Bound the Hartshorne-Speiser-Lyubeznik invariant for hypersurface singularities

Establish connections between characteristic zero and positive characteristic invariants

Abstract

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.