The higher K-theory of a complex surface, by Claudio Pedrini and Charles A. Weibel

Let X be a smooth complex variety of dimension at most two, and let F be its function field. We prove that the K-groups of F are divisible above the dimension of X, and that the K-groups of X are divisible-by-finite.

We also describe the torsion in the K-groups of F and X. The classical Betti cohomology of X completely describes this torsion.

This paper appeared in Compositio Math. 129 (2001), 239-271.

Claudio Pedrini <>
Charles A. Weibel <>