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.
Zero-cycle groups on algebraic varieties / F. Binda, A. Krishna. - In: JOURNAL DE L'ÉCOLE POLYTECHNIQUE. MATHÉMATIQUES. - ISSN 2270-518X. - 9(2022), pp. 281-325. [10.5802/jep.183]
Zero-cycle groups on algebraic varieties
F. Binda
;
2022
Abstract
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.File | Dimensione | Formato | |
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JEP_2022__9__281_0.pdf
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