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In 1969, Mumford  proved that, for a complete non-singular algebraic surfaceFover the complex number fieldC, the dimension of the Chow group of zero-cycles onFis infinite if the geometric genus ofFis positive. To this end, he defined a regular 2-formηfon a non-singular varietySfor a regular 2-formηonFand for a morphismf:S→SnF, whereSnFis the 72-th symmetric product ofF, and he showed thatηfvanishes if all 0-cyclesf(s), s ∈ S, are rationally equivalent. Roitman  later generalized this to adoi:10.1017/s002776300002081x fatcat:3iohbj7yfbeujoxx4msw4n3fa4