Higher direct images of snc ideal sheaves

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.

arXiv commentComments welcome! V2: title updated to more specifically describe results, some repetitive parts of proofs consolidated into lemmas. V3: added necessary conjecture on existence of normal Cohen-Macaulayfications