Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T04:16:33.128Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)