Grothendieck ’ s pairing on component groups of Jacobians

@inproceedings{Bosch2002GrothendieckS,
  title={Grothendieck ’ s pairing on component groups of Jacobians},
  author={Siegfried Bosch and Dino Lorenzini},
  year={2002}
}
Let R be a discrete valuation ring with field of fractions K . Let AK be an abelian variety over K with dual AK . Denote by A and A ′ the corresponding Néron models and by ΦA and ΦA′ their component groups. In [Gr], Exp. VII–IX, Grothendieck used the notion of biextension invented by Mumford to investigate how the duality between AK and AK is reflected on the level of Néron models. In fact, the essence of the relationship between A and A′ is captured by a bilinear pairing 〈 , 〉 : ΦA × ΦA′ −→ Q… CONTINUE READING

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