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suslin homology

Journal of the Institute of Mathematics of Jussieu (1)

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ZERO-CYCLES ON NORMAL PROJECTIVE VARIETIES
Part of
Mainak Ghosh, Amalendu Krishna
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 22 / Issue 5 / September 2023

Published online by Cambridge University Press:

11 February 2022, pp. 2241-2295

Print publication:

September 2023
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We 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 missing p-part in the torsion theorem of Spieß and Szamuely.