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arXiv · 0710.3147

Local acyclic fibrations and the de Rham complex

Ben Lee
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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.

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Ben Lee. 2007-10-22. Local acyclic fibrations and the de Rham complex. https://arxiv.org/abs/0710.3147

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