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.
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.
@article{AIF_1997__47_5_1257_0, 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}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1599/} }
TY - JOUR AU - Bosch, Siegfried TI - Component groups of abelian varieties and Grothendieck's duality conjecture JO - Annales de l'Institut Fourier PY - 1997 SP - 1257 EP - 1287 VL - 47 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1599/ DO - 10.5802/aif.1599 LA - en ID - AIF_1997__47_5_1257_0 ER -
%0 Journal Article %A Bosch, Siegfried %T Component groups of abelian varieties and Grothendieck's duality conjecture %J Annales de l'Institut Fourier %D 1997 %P 1257-1287 %V 47 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1599/ %R 10.5802/aif.1599 %G en %F AIF_1997__47_5_1257_0
Bosch, Siegfried. Component groups of abelian varieties and Grothendieck's duality conjecture. Annales de l'Institut Fourier, Volume 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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