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arXiv · 2012.11249

Zero-cycles on normal varieties

Mainak Ghosh·Amalendu Krishna
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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.

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Mainak Ghosh, Amalendu Krishna. 2020-12-21. Zero-cycles on normal varieties. https://arxiv.org/abs/2012.11249

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