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ZERO-CYCLES ON NORMAL PROJECTIVE VARIETIES

Part of: $K$-theory in geometry Cycles and subschemes (Co)homology theory

Published online by Cambridge University Press:  11 February 2022

Mainak Ghosh  and
Amalendu Krishna Open the ORCID record for Amalendu Krishna [Opens in a new window]
Mainak Ghosh
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400005, India (mainak@math.tifr.res.in)
Amalendu Krishna*
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
*
amalenduk@iisc.ac.in
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Abstract

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.

Keywords

singular varietiesalgebraic cyclesclass field theorySuslin homologyLefschetz theorems

MSC classification

Primary: 14C25: Algebraic cycles
Secondary: 14F42: Motivic cohomology; motivic homotopy theory 19E15: Algebraic cycles and motivic cohomology

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2241 - 2295
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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