Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory

Federico Binda; Amalendu Krishna; Shuji Saito

Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory

Algebraic Geometry 2021-08-25 v3

Authors: Federico Binda , Amalendu Krishna , Shuji Saito

Abstract

We prove Bloch's formula for the Chow group of 0-cycles with modulus on a smooth quasi-projective surface over a field. We use this formula to give a simple proof of the rank one case of a conjecture of Deligne and Drinfeld on lisse $\overline{\mathbb{Q}}_{\ell}$ -sheaves. This was originally solved by Kerz and Saito in characteristic $\neq 2$ .

Keywords

algebraic cycles and chow groups

Cite

@article{arxiv.2002.01856,
  title  = {Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory},
  author = {Federico Binda and Amalendu Krishna and Shuji Saito},
  journal= {arXiv preprint arXiv:2002.01856},
  year   = {2021}
}

Comments

47 pages. Final version, to appear in J. Algebraic Geom. (JAG)

Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory

Abstract

Keywords

Cite

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