The Torsion of the Group of 0-Cycles Modulo Rational Equivalence

Abstract

In this work we continue the study of rational equivalence of O-cycles on nonsingular projective varieties over an algebraically closed field k, which we began in [13], [14]. The main result of this work is the calculation of the group of finite order O-cycles modulo rational equivalence. Except possibly for p-torsion if char k = p > 0, this group is equal to the group of points of finite order on the Albanese variety. We shall always use the following notation (we do not suppose here that X is nonsingular): Z0(X)-the group of O-cycles on the projective variety X; ZO(X) c Z0(X) the subgroup of cycles of degree 0; Z+(X) c Z0(X) the semigroup of effective cycles; SX the n-fold symmetric product of X, SzX= Xn/=n; S(X/S)-the n-fold relative symmetric product of X ->