From Sheaf Cohomology to the Algebraic de Rham Theorem
Algebraic Geometry
2014-01-14 v3
Abstract
Let X be a smooth complex algebraic variety with the Zariski topology, and let Y be the underlying complex manifold with the complex topology. Grothendieck's algebraic de Rham theorem asserts that the singular cohomology of Y with complex coefficients can be computed from the complex of sheaves of algebraic differential forms on X. This article gives an elementary proof of Grothendieck's algebraic de Rham theorem, elementary in the sense that we use only tools from standard textbooks as well as Serre's FAC and GAGA papers.
Cite
@article{arxiv.1302.5834,
title = {From Sheaf Cohomology to the Algebraic de Rham Theorem},
author = {Fouad El Zein and Loring W. Tu},
journal= {arXiv preprint arXiv:1302.5834},
year = {2014}
}
Comments
53 pages; this version replaces an earlier version submitted in August 2013. Some misprints have been corrected