Higher direct images of snc ideal sheaves

TL;DR

This paper proves invariance of cohomology groups of snc ideal sheaves under certain birational transformations in arbitrary characteristic, extending foundational results in rational pairs theory assuming Cohen-Macaulayfication conjecture.

Contribution

It establishes cohomology invariance for snc ideal sheaves in arbitrary characteristic and extends rational pairs theory beyond characteristic zero.

Findings

Cohomology invariance under specific birational morphisms.

Extension of rational pairs results to positive characteristic.

Conditional results based on Cohen-Macaulayfication conjecture.

Abstract

We prove invariance results for the cohomology groups of ideal sheaves of simple normal crossing divisors under (a restricted class of) birational morphisms of pairs in arbitrary characteristic, assuming a conjecture regarding the existence of normal Cohen-Macaulayfications. As an application, we extend some foundational results in the theory of rational pairs that were previously known only in characteristic 0.