Representability of Chow Zero-Cycles

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I'll discuss Mumford's beautiful paper "Rational Equivalence of 0-Cycles on Surfaces," which amounts to a counter-example to Severi's implicit claim that the set of Chow 0-cycles on a surface, up to rational equivalence, is representable.  Mumford shows that this cannot be the case if the surface admits a non-vanishing regular 2-form.  Time permitting, I'll discuss related results of Roitman, and work on a converse conjectured by Bloch