Torsion in the Chow group of codimension two: the case of varieties with isolated singularities.Proceedings of the Luminy conference on algebraic K-theory (Luminy, 1983).

Let Y be an irreducible quasiprojective variety over an algebraically closed field and let n be an integer prime to the characteristic. The main result of this paper is: If Y has only isolated singularities, then nCH2(Y ) is finite. The basic idea of the proof follows the plan laid down by S. Bloch for the nonsingular case, eventually relying on the work of A. S. Merkurev and A. A. Suslin . The technical difficulties for the setting of the present paper are overcome by replacing certain terms in the Gersten complex by sheaves which miss the singular locus sufficiently to get an acyclic resolution but still retain enough information to compute the Chow group.