arXiv:0710.3147 Abstract | arXiv Analytics

arXiv:0710.3147 [math.AG]Abstract References Reviews Resources

Local acyclic fibrations and the de Rham complex

Published 2007-10-16, updated 2007-10-22Version 2

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.

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

Categories: math.AG, math.AT

Subjects: 14F40, 55N30

Keywords: rham complex, arbitrary local acyclic fibrations, extend cech cohomology, possibly singular complex variety, main technique

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