Zero-cycle groups on algebraic varieties

@article{Binda2021ZerocycleGO,
  title={Zero-cycle groups on algebraic varieties},
  author={Federico Binda and Amalendu Krishna},
  journal={Journal de l’{\'E}cole polytechnique — Math{\'e}matiques},
  year={2021}
}
  • F. BindaA. Krishna
  • Published 16 April 2021
  • Mathematics
  • Journal de l’École polytechnique — Mathématiques
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… 

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We prove an extension of the Kato-Saito unramified class field theory for smooth projective schemes over a finite field to a class of normal projective schemes. As an application, we obtain Bloch’s

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Abstract We prove that for a smooth projective variety X of dimension d defined over a finite field k, the structure map σ : X → Spec k induces an isomorphism σ∗ : CH d+1(X, 1) ≅ CH 1(k, 1) = k*. We
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