Semi-topological cycle theory I

2010/01/14 by Teh, J. H.
#14C25 #19E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1001.2355

Abstract

We study algebraic varieties parametrized by topological spaces and enlarge the domains of Lawson homology and morphic cohomology to this category. We prove a Lawson suspension theorem and splitting theorem. A version of Friedlander-Lawson moving is obtained to prove a duality theorem between Lawson homology and morphic for smooth semi-topological projective varieties. K-groups for semi-topological projective varieties and Chern classes are also constructed.

Related

• Semi-topological K-theory for certain projective varieties
• A homology and cohomology theory for real projective varieties
• Lawson Homology for Abelian Varieties
• Lawson Homology for projective varieties with C^*-action
• A note on Lawson homology for smooth varieties with small Chow groups