#### Volume 14, issue 5 (2014)

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Bigraded invariants for real curves

### Pedro F dos Santos and Paulo Lima-Filho

Algebraic & Geometric Topology 14 (2014) 2809–2852
##### Abstract

For a proper smooth real algebraic curve $\Sigma$ we compute the ring structure of both its ordinary bigraded $Gal\left(ℂ∕ℝ\right)$–equivariant cohomology [Bull. Amer. Math. Soc. 4 (1981) 208–212] and its integral Deligne cohomology for real varieties [Math. Ann. 350 (2011) 973–1022]. These rings reflect both the equivariant topology and the real algebraic structure of $\Sigma$ and they are recipients of natural transformations from motivic cohomology. We conjecture that they completely detect the motivic torsion classes.

##### Keywords
equivariant cohomology, Deligne cohomology, real varieties, real curves
Primary: 55N91
Secondary: 14P25
##### Publication
Received: 2 August 2013
Revised: 14 January 2014
Accepted: 5 February 2014
Published: 6 November 2014
##### Authors
 Pedro F dos Santos Departamento de Matemática Instituto Superior Técnico Universidade de Lisboa Avenida Rovisco Pais 1049-001 Lisboa Portugal http://www.math.tecnico.ulisboa.pt/~pedfs Paulo Lima-Filho Department of Mathematics Texas A&M University Mailstop 3368 College Station, TX 77843 USA http://www.math.tamu.edu/~plfilho