ZERO-CYCLES ON NORMAL PROJECTIVE VARIETIES

Abstract

AbstractWe prove an extension of the Kato–Saito unramified class field theory for smooth projective schemes over a finite field to a class of normal projective schemes. As an application, we obtain Bloch’s formula for the Chow groups of$0$-cycles on such schemes. We identify the Chow group of$0$-cycles on a normal projective scheme over an algebraically closed field to the Suslin homology of its regular locus. Our final result is a Roitman torsion theorem for smooth quasiprojective schemes over algebraically closed fields. This completes the missingp-part in the torsion theorem of Spieß and Szamuely.