Let be the Jacobian variety of the Drinfeld modular curve over , where is an ideal in . Let be an exact sequence of abelian varieties. Assume , as a subvariety of , is stable under the action of the Hecke algebra End . We give a criterion which is sufficient for the exactness of the induced sequence of component groups of the Néron models of these abelian varieties over . This criterion is always satisfied when either or is one-dimensional. Moreover, we prove that the sequence of component groups is always exact on -power torsion for any prime not dividing . In particular, the sequence is always exact when .
Soit la variété Jacobienne de la courbe modulaire de Drinfeld sur , où est un idéal de . Soit une suite exacte de variétés abéliennes. Supposons que , comme sous-variété de , est stable sous l’action de l’algèbre de Hecker End . Nous donnons un critère suffisant pour l’exactitutde de la suite induite du groupe de composants connexe des modèles de Néron de ces variétés abéliennes sur . Ce critère est toujours satisfait si ou est de dimension . De plus, nous démontrons que la suite des parties de -torsion des groupes de composantes connexes est exacte pour tout nombre premier ne divisant pas . En particulier, cette suite est exacte quand .
Keywords: Component groups, Drinfeld modular curves, monodromy pairing
Mot clés : groupe de composants, courbe modulaire de Drinfeld, monodromie
Papikian, Mihran 1
@article{AIF_2004__54_7_2163_0, author = {Papikian, Mihran}, title = {On component groups of {Jacobians} of {Drinfeld} modular curves}, journal = {Annales de l'Institut Fourier}, pages = {2163--2199}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {7}, year = {2004}, doi = {10.5802/aif.2078}, zbl = {1071.11034}, mrnumber = {2139692}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2078/} }
TY - JOUR AU - Papikian, Mihran TI - On component groups of Jacobians of Drinfeld modular curves JO - Annales de l'Institut Fourier PY - 2004 SP - 2163 EP - 2199 VL - 54 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2078/ DO - 10.5802/aif.2078 LA - en ID - AIF_2004__54_7_2163_0 ER -
%0 Journal Article %A Papikian, Mihran %T On component groups of Jacobians of Drinfeld modular curves %J Annales de l'Institut Fourier %D 2004 %P 2163-2199 %V 54 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2078/ %R 10.5802/aif.2078 %G en %F AIF_2004__54_7_2163_0
Papikian, Mihran. On component groups of Jacobians of Drinfeld modular curves. Annales de l'Institut Fourier, Volume 54 (2004) no. 7, pp. 2163-2199. doi : 10.5802/aif.2078. https://aif.centre-mersenne.org/articles/10.5802/aif.2078/
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