Displaying similar documents to “Weil-Châtelet groups over local fields : addendum”

Component groups of abelian varieties and Grothendieck's duality conjecture

Siegfried Bosch (1997)

Annales de l'institut Fourier

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We investigate Grothendieck’s pairing on component groups of abelian varieties from the viewpoint of rigid uniformization theory. Under the assumption that the pairing is perfect, we show that the filtrations, as introduced by Lorenzini and in a more general way by Bosch and Xarles, are dual to each other. Furthermore, the methods yield some progress on the perfectness of the pairing itself, in particular, for abelian varieties with potentially multiplicative reduction.