Integral Deligne Cohomology for Real Varieties
Algebraic Geometry
2008-10-14 v1 K-Theory and Homology
Abstract
We develop an integral version of Deligne cohomology for smooth proper real varieties. For this purpose the role played by singular cohomology in the complex case has to be replaced by ordinary bigraded G-equivariant cohomology, where G=Gal(C/R). This is the G-equivariant counterpart of singular cohomology. We establish the basic properties of the theory and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2.
Cite
@article{arxiv.0810.2058,
title = {Integral Deligne Cohomology for Real Varieties},
author = {Pedro F. dos Santos and Paulo Lima-Filho},
journal= {arXiv preprint arXiv:0810.2058},
year = {2008}
}