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Zero-cycle groups on algebraic varieties

Binda, F and Krishna, A (2022) Zero-cycle groups on algebraic varieties. In: Journal de l'Ecole Polytechnique - Mathematiques, 9 . pp. 281-325.

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Official URL: https://doi.org/10.5802/JEP.183


We compare various groups of 0-cycles on quasi-projective varieties over a field. As applications, we show that for certain singular projective varieties, the Levine-Weibel Chow group of 0-cycles coincides with the corresponding Friedlander-Voevodsky motivic cohomology. We also show that over an algebraically closed field of positive characteristic, the Chow group of 0-cycles with modulus on a smooth projective variety with respect to a reduced divisor coincides with the Suslin homology of the complement of the divisor. We prove several generalizations of the finiteness theorem of Saito and Sato for the Chow group of 0-cycles over p-adic fields. We also use these results to deduce a torsion theorem for Suslin homology which extends a result of Bloch to open varieties.

Item Type: Journal Article
Publication: Journal de l'Ecole Polytechnique - Mathematiques
Publisher: Ecole Polytechnique
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Cycles on singular varieties; Cycles with modulus; Motivic cohomology
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 08 Jul 2022 09:39
Last Modified: 08 Jul 2022 09:39
URI: https://eprints.iisc.ac.in/id/eprint/74323

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