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- W4293493489 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper Q overbar Subscript script l> <mml:semantics> <mml:msub> <mml:mover> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>Q</mml:mi> </mml:mrow> <mml:mo accent=false>¯<!-- ¯ --></mml:mo> </mml:mover> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>ℓ<!-- ℓ --></mml:mi> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>overline {mathbb {Q}}_{ell }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-sheaves. This was originally solved by Kerz and Saito in characteristic <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=not-equals 2> <mml:semantics> <mml:mrow> <mml:mo>≠<!-- ≠ --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>neq 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W4293493489 date "2022-08-29" @default.
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- W4293493489 title "Bloch’s formula for 0-cycles with modulus and higher-dimensional class field theory" @default.
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- W4293493489 doi "https://doi.org/10.1090/jag/792" @default.
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