Pullback of regular singular stratified bundles and restriction to curves

TL;DR

This paper proves that regular singularity of stratified bundles in positive characteristic is preserved under pullback and can be verified on curves when the ground field is sufficiently large.

Contribution

It establishes the stability of regular singularity under pullback and reduces the verification to curves in large fields, advancing understanding of stratified bundles in positive characteristic.

Findings

Regular singularity is preserved by pullback.

Regular singularity can be checked on curves in large fields.

Provides criteria for stratified bundles in positive characteristic.

Abstract

A stratified bundle is a vector bundle which is a D-module. We show that regular singularity of stratified bundles on smooth varieties in positive characteristic is preserved by pullback and that regular singularity can be checked on curves, if the ground field is large enough.