Differential forms on log canonical spaces in positive characteristic

Abstract

Given a logarithmic $1$-form on the snc locus of a log canonical surface pair $(X,D)$ over a perfect field of characteristic $p\ge 7$, we show that it extends with at worst logarithmic poles to any resolution of singularities. We also prove the analogous statement for regular differential forms, under an additional tameness hypothesis. In addition, residue and restriction sequences for tamely dlt pairs are established. We give a number of examples showing that our results are sharp in the surface case, and that they fail in higher dimensions. On the other hand, our techniques yield a new proof of the characteristic zero Logarithmic Extension Theorem in any dimension.

References in corpus (1)

• Extending holomorphic forms from the regular locus of a complex space to a resolution of singularities

Cited by in corpus (5)

• Bogomolov--Sommese type vanishing for globally $F$-regular threefolds
• Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic
• Weak Akizuki-Nakano vanishing theorem for globally $F$-split 3-folds
• On singularity types of del Pezzo surfaces with rational double points in positive characteristic
• The Violation of the Lipman-Zariski conjecture in positive characteristic