Kato homology of arithmetic schemes and higher class field theory over local fields.
Jannsen, Uwe, Saito, Shuji (2003)
Documenta Mathematica
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Displaying similar documents to “The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality.”
Kato homology of arithmetic schemes and higher class field theory over local fields.
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In this paper the equality is established of three different pairings between the first de Rham cohomology group of an abelian scheme over a base flat over and that of its dual. These pairings have appeared and been used either explicitly or implicitly in the literature. In the last section we deduce a generalization to arbitrary characteristic of Serre’s formula for the Poincaré pairing on the first de Rham cohomology group of a curve over a field of characteristic zero. ...