We compare various groups of -cycles on quasi-projective varieties over a field. As applications, we show that for certain singular projective varieties, the Levine-Weibel Chow group of -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 -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 -cycles over -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 -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 -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 -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 -cycles sur les corps -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.
@article{JEP_2022__9__281_0, author = {Federico Binda and Amalendu Krishna}, title = {Zero-cycle groups on algebraic varieties}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {281--325}, publisher = {\'Ecole polytechnique}, volume = {9}, year = {2022}, doi = {10.5802/jep.183}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.183/} }
TY - JOUR TI - Zero-cycle groups on algebraic varieties JO - Journal de l’École polytechnique — Mathématiques PY - 2022 DA - 2022/// SP - 281 EP - 325 VL - 9 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.183/ UR - https://doi.org/10.5802/jep.183 DO - 10.5802/jep.183 LA - en ID - JEP_2022__9__281_0 ER -
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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