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

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 $\ne 2$.

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

References in corpus (2)

• Zero cycles with modulus and zero cycles on singular varieties
• K-theory and 0-cycles on schemes