4.3 Article

BLOCH'S FORMULA FOR 0-CYCLES WITH MODULUS AND HIGHER-DIMENSIONAL CLASS FIELD THEORY

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JOURNAL OF ALGEBRAIC GEOMETRY
Volume -, Issue -, Pages -

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UNIV PRESS INC
DOI: 10.1090/jag/792

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We prove a specific case of Bloch's formula and use it to prove a conjecture by Deligne and Drinfeld regarding lisse (Q) over bar (l)-sheaves.
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.

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