Homology, Homotopy and Applications

Local acyclic fibrations and the de Rham complex

Ben Lee

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.hha/1251832562

Mathematical Reviews number (MathSciNet)
MR2506129

Zentralblatt MATH identifier
1172.14012

Subjects
Primary: 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10] 55N30: Sheaf cohomology [See also 18F20, 32C35, 32L10]

Keywords
Simplicial presheaves de Rham cohomology homotopy

Citation

Lee, Ben. Local acyclic fibrations and the de Rham complex. Homology Homotopy Appl. 11 (2009), no. 1, 115--140. https://projecteuclid.org/euclid.hha/1251832562


Export citation