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.
Publié le : 2009-05-15
Classification:
Simplicial presheaves,
de Rham cohomology,
homotopy,
14F40,
55N30
@article{1251832562,
author = {Lee, Ben},
title = {Local acyclic fibrations and the de Rham complex},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 115-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832562}
}
Lee, Ben. Local acyclic fibrations and the de Rham complex. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 115-140. http://gdmltest.u-ga.fr/item/1251832562/