Bloch’s formula for 0-cycles with modulus and higher-dimensional class field theory

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 (Q) over bar (l)-sheaves. This was originally solved by Kerz and Saito in characteristic not equal 2.