## Homology, Homotopy and Applications

### Local acyclic fibrations and the de Rham complex

Ben Lee

#### Abstract

We reinterpret algebraic de Rham cohomology for a possibly singular complex variety $X$ as sheaf cohomology in the site of smooth schemes over $X$ with Voevodsky's $h$-topology. Our results extend to the algebraic de Rham complex as well. Our main technique is to extend Cech cohomology of hypercovers to arbitrary local acyclic fibrations of simplicial presheaves.

#### Article information

Source
Homology Homotopy Appl., Volume 11, Number 1 (2009), 115-140.

Dates
First available in Project Euclid: 1 September 2009