Zero-cycle groups on algebraic varieties
Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 281-325.

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.

Nous comparons divers groupes de 0-cycles sur des variétés quasi-projectives sur un corps. Comme applications, nous montrons que pour certaines variétés projectives singulières, le groupe de Chow de Levine-Weibel des 0-cycles coïncide avec la cohomologie motivique correspondante de Friedlander-Voevodsky. Nous montrons également que sur un corps algébriquement clos de caractéristique positive, le groupe de Chow des 0-cycles avec modulus sur une variété projective lisse par rapport à un diviseur réduit coïncide avec l’homologie de Suslin du complémentaire du diviseur. Nous prouvons plusieurs généralisations du théorème de finitude de Saito et Sato pour le groupe de Chow des 0-cycles sur les corps p-adiques. Nous utilisons également ces résultats pour déduire un théorème de torsion pour l’homologie de Suslin qui étend un résultat de Bloch aux variétés ouvertes.

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DOI: 10.5802/jep.183
Classification: 14C25, 14F42, 19E15
Keywords: Cycles with modulus, cycles on singular varieties, motivic cohomology
Mot clés : Cycles avec modulus, cycles sur les variétés singulières, cohomologie motivique

Federico Binda 1; Amalendu Krishna 2

1 Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano Via Cesare Saldini 50, 20133 Milano, Italy
2 Department of Mathematics, Indian Institute of Science Bangalore, 560012, India
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Federico Binda; Amalendu Krishna. Zero-cycle groups on algebraic varieties. Journal de l’École polytechnique — Mathématiques, Volume 9 (2022), pp. 281-325. doi : 10.5802/jep.183. https://jep.centre-mersenne.org/articles/10.5802/jep.183/

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