Semi-topological K-theory for certain projective varieties

In this paper we compute Lawson homology groups and semi-topological K-theory for some threefolds and fourfolds. We consider smooth complex projective varieties whose zero cycles are supported on a proper subvariety. Rationally connected varieties are examples of such varieties. The computation makes use of a technique of Bloch and Srinavas, of the Bloch-Kato conjecture and of the spectral sequence relating morphic cohomology and semi-topological K-theory.