Volume 14, issue 5 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 Σ we compute the ring structure of both its ordinary bigraded Gal()–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 Σ 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
Mathematical Subject Classification 2010
Primary: 55N91
Secondary: 14P25
References
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