Integral Deligne Cohomology for Real Varieties

Details Integral Deligne Cohomology for Real Varieties Integral Deligne Cohomology for Real Varieties

2008-10-13

arxiv.org/abs/0810.2058v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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