Zero-cycles on normal varieties

Abstract

We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. 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 quasi-projective schemes over algebraically closed fields. This completes the missing $p$-torsion part in the torsion theorem of Spiess and Szamuely.

arXiv commentFinal version, 44 pages, to appear in `Journal of the Institute of Mathematics of Jussieu'

References in corpus (6)

• Revêtements étales et groupe fondamental (SGA 1)
• Chow group of 0-cycles with modulus and higher dimensional class field theory
• Zero cycles with modulus and zero cycles on singular varieties
• Duality of Albanese and Picard 1-motives
• Bivariant theories in motivic stable homotopy
• K-theory and 0-cycles on schemes