Semi-topological K-theory for certain projective varieties

In this paper we compute Lawson homology groups and semi-topological K-theory for certain 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 different techniques of decomposition of the diagonal cycle, of the Bloch–Kato conjecture and of the spectral sequence relating morphic cohomology and semi-topological K-theory.