no. 5
Component groups of abelian varieties and Grothendieck's duality conjecture
Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1257-1287.

Nous étudions l’accouplement de Grothendieck sur les groupes des composantes des variétés abéliennes, en utilisant le point de vue de l’uniformisation rigide. Supposant que l’accouplement est parfait, nous démontrons que les filtrations, introduites par Lorenzini et d’une manière plus générale par Bosch et Xarles, sont duales l’une de l’autre. Les méthodes appliquées permettent de progresser sur le problème de la perfection de l’accouplement, surtout pour les variétés abéliennes avec réduction potentiellement multiplicative.

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.

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     author = {Bosch, Siegfried},
     title = {Component groups of abelian varieties and {Grothendieck's} duality conjecture},
     journal = {Annales de l'Institut Fourier},
     pages = {1257--1287},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {47},
     number = {5},
     year = {1997},
     doi = {10.5802/aif.1599},
     mrnumber = {98k:14061},
     zbl = {0919.14026},
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     url = {http://www.numdam.org/articles/10.5802/aif.1599/}
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Bosch, Siegfried. Component groups of abelian varieties and Grothendieck's duality conjecture. Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1257-1287. doi : 10.5802/aif.1599. http://www.numdam.org/articles/10.5802/aif.1599/

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