Mathematische Annalen

, Volume 350, Issue 4, pp 973–1022 | Cite as

Integral Deligne cohomology for real varieties

  • Pedro F. dos SantosEmail author
  • Paulo Lima-Filho


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 the ordinary bigraded \({Gal(\mathbb{C}/{\mathbb{R}})}\)-equivariant cohomology of Lewis et al. (Bull Am Math Soc (N.S.) 4(2):208–212, 1981), the equivariant counterpart of singular cohomology. The theory is aimed at giving more precise information about the 2-primary components of regulators. We establish basic properties and give a geometric interpretation for the groups in dimension 2 in weights 1 and 2.


Exact Sequence Line Bundle Real Variety Equivariant Cohomology Holomorphic Line Bundle 
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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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