Differential forms in the h-topology

TL;DR

This paper explores sheaves of differential forms and their cohomology within the h-topology, extending classical results to singular varieties and applications in the Minimal Model Program and de Rham cohomology.

Contribution

It introduces a framework for studying differential forms in the h-topology, broadening the scope from smooth to singular varieties with new applications.

Findings

Extended cohomology results to singular varieties

Applied to singularities in the Minimal Model Program

Analyzed de Rham cohomology in the h-topology

Abstract

We study sheaves of differential forms and their cohomology in the h-topology. This allows to extend standard results from the case of smooth varieties to the general case. As a first application we explain the case of singularities arising in the Minimal Model Program. As a second application we consider de Rham cohomology.