### Roitman's theorem for singular complex projective surfaces, by Luca Barbieri-Viale, Claudio Pedrini, and Charles Weibel

Let X be a complex projective surface, not necessarily smooth. We construct
and study a natural map from the Chow group of smooth zero-cycles on X to
Griffith's Intermediate Jacobian. Our main result is that this is an
isomorphism modulo torsion.

The Intermediate Jacobian is an extension of an abelian variety by a torus (a
1-motive), so its torsion subgroup is easily determined. If X is smooth, our
map is the classical Abel-Jacobi map and our main result reduces to Roitman's
Theorem. If X is normal, our result follows from work of Collino and Levine.
Our main tool is the Chern class from K-theory to Deligne-Beilinson
cohomology.

This has appeared in Duke J. Math., 84 (1996), 155-190.

Luca Barbieri-Viale <barbieri@dima.unige.it>

Claudio Pedrini <pedrini@dima.unige.it>

Charles Weibel <weibel@math.rutgers.edu>