Local acyclic fibrations and the de Rham complex

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.

Keywords

simplicial presheaves, de Rham cohomology, homotopy

2010 Mathematics Subject Classification

14F40, 55N30

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Published 1 January 2009