Zero-cycle groups on algebraic varieties
Federico Binda, Amalendu Krishna

TL;DR
This paper investigates various groups of 0-cycles on algebraic varieties, establishing their relationships and equivalences in different contexts, and extends several finiteness and torsion results in algebraic geometry.
Contribution
It demonstrates the equivalence of Levine-Weibel Chow groups with motivic cohomology for certain singular varieties and generalizes finiteness theorems for 0-cycle groups over p-adic fields.
Findings
Levine-Weibel Chow group coincides with motivic cohomology for some singular varieties
Finiteness theorems for Chow groups over p-adic fields are extended
A torsion theorem for Suslin homology is established
Abstract
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 -adic fields. We also use these results to deduce a torsion theorem for Suslin homology which extends a result of Bloch to open varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
