Local acyclic fibrations and the de Rham complex

Details Local acyclic fibrations and the de Rham complex Local acyclic fibrations and the de Rham complex

2007-10-16

arxiv.org/abs/0710.3147v2

Mathematics

Algebraic Geometry

24 pages; exposition revised, typos fixed, minor amendments to statements

Scientific paper

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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