English

Local acyclic fibrations and the de Rham complex

Algebraic Geometry 2007-10-23 v2 Algebraic Topology

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.

Keywords

Cite

@article{arxiv.0710.3147,
  title  = {Local acyclic fibrations and the de Rham complex},
  author = {Ben Lee},
  journal= {arXiv preprint arXiv:0710.3147},
  year   = {2007}
}

Comments

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

R2 v1 2026-06-21T09:32:44.259Z