We compute Lawson homology groups and semi-topological K-theory for certain "degenerate" varieties. "Degenerate" varieties are those smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. Our main method of study makes use of a technique of Bloch and Srinivas, of the Bloch-Kato conjecture and of the spectral sequence relating morphic cohomology and semi-topological K-theory. In the end of the thesis we focus on the understanding of Lawson homology of generic hypersurfaces of small degree. Our method is based on the fact that for a certain class of hypersurfaces the cylindrical correspondence homomorphism on Lawson homology is a surjection and it is an extension of a method first used by J. Lewis in his study of Chow groups of small degree hypersurfaces.

Last modified

• 05/25/2018

Creator

• Mircea Alexandru Voineagu

DOI

• https://doi.org/10.21985/N2012M

Subject

• Mathematics

Keyword

• algebraic cycles
• semi-topological K-theory
• Lawson homology

Date created

• 2007-04-25

Resource type

• Dissertation

Rights statement

• In Copyright