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ALGEBRAIC CYCLES ON REAL VARIETIES AND ℤ/2-EQUIVARIANT HOMOTOPY THEORY

Published online by Cambridge University Press:  06 March 2003

PEDRO F. DOS SANTOS
PEDRO F. DOS SANTOS
Affiliation:
Department of Mathematics, Texas A&M University, USA. Current address: Departamento de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001 Lisbon, Portugal. [email protected]
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Abstract

In this paper the spaces of algebraic cycles on a real projective variety $X$ are studied as $\mathbb{Z}/2$-spaces under the action of the Galois group ${\rm Gal}(\mathbb{C}/\mathbb{R})$. In particular, the equivariant homotopy type of the group of algebraic $p$-cycles $\mathcal{Z}_p(\mathbb{P}_{\mathbb{C}}^n)$ is computed. A version of Lawson homology for real varieties is proposed. The real Lawson homology groups are computed for a class of real varieties.

2000 Mathematical Subject Classification: primary 55P91; secondary 14C05, 19L47, 55N91.

Keywords

algebraic cyclesequivariant homologyLawson homology
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 86 , Issue 2 , March 2003 , pp. 513 - 544
Copyright
2003 London Mathematical Society

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