The universal regular quotient of the Chow group of 0-cycles on a singular projective variety

Abstract

We show the existence of a regular universal quotient as a smooth commutative algebraic group of the Chow group of 0-cycles on a projective reduced variety, and give over the field of complex numbers an analytic description of it. This generalizes the classical theory of the Albanese. The Chow group of 0-cycles is then isomorphic to this smooth algebraic group if and only if it is finite dimensional in the sense of Mumford. This generalizes the classical theorem of Roitman.