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arXiv · 2002.01856

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

Federico Binda·Amalendu Krishna·Shuji Saito
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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 $\neq 2$.

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Federico Binda, Amalendu Krishna, Shuji Saito. 2020-02-05. Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory. https://arxiv.org/abs/2002.01856

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