### On K_1 and K_2 of algebraic surfaces (with an appendix by A. Collino), by Stefan Mueller-Stach (Essen) and Shuji Saito (Nagano)

We study the higher Chow groups CH^2(X,1) and CH^3(X,2) of smooth, projective
algebraic surfaces over a field of char 0. We develop a theoretical
framework to study them by using so-called higher normal functions and higher
infinitesimal invariants when the cycles are supported on normal crossing
divisors. Then we investigate their structure on hypersurfaces in projective
3-space. This leads to vanishing or decomposbility results. On the other
hand we find examples of these groups in degrees 4 and 5 where the result is
a highly indecomposably (hence big) abelian group. Part of the examples are
due to Alberto Collino.

Stefan Mueller-Stach (Essen) <mueller-stach@uni-essen.de>

Shuji Saito (Nagano) <sshuji@msb.biglobe.ne.jp>