Homology, Homotopy and Applications

Volume 11 (2009)

Number 1

Local acyclic fibrations and the de Rham complex

Pages: 115 – 140

DOI: https://dx.doi.org/10.4310/HHA.2009.v11.n1.a6


Ben Lee


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.


simplicial presheaves, de Rham cohomology, homotopy

2010 Mathematics Subject Classification

14F40, 55N30

Published 1 January 2009