Algebraic cycles on real varieties and Z(2)-equivariant homotopy theory.

摘要

In Chapter 1 of this dissertation we study spaces of algebraic cycles on a Real projective variety X. We consider these spaces with the Z2 -action induced from the Real structure on X. When X is PnC these spaces are products of classifying spaces for Z2 -equivariant cohomology with coefficients in the constant Mackey functor Z . We prove this by establishing an equivariant version of the classical Dold-Thom theorem. We also propose a version of Lawson homology for Real varieties and compute it in some examples. In Chapter 2 we relate Z 2-equivariant cohomology with Z coefficients to certain Galois-Grothendieck cohomology groups which are invariants frequently used in real algebraic geometry.