[Sur les représentations galoisiennes associées aux variétés abéliennes non simples]
Nous étudions les représentations galoisiennes associées aux variétés abéliennes non simples définies sur des corps de type fini de caractéristique quelconque. Nous donnons des conditions suffisantes pour que ces représentations se décomposent en produit et nous les utilisons pour montrer des analogues arithmétiques de certains résultats antérieurs de Moonen et Zarhin concernant les variétés abéliennes complexes (de dimension au plus 5).
We study Galois representations attached to nonsimple abelian varieties over finitely generated fields of arbitrary characteristic. We give sufficient conditions for such representations to decompose as a product, and apply them to prove arithmetical analogues of results shown by Moonen and Zarhin in the context of complex abelian varieties (of dimension at most 5).
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Keywords: Tate classes, Hodge group, Galois representations, abelian varieties, Mumford-Tate conjecture
Mot clés : classes de Tate, groupe de Hodge, représentations de Galois, variétés abéliennes, conjecture de Mumford-Tate
Lombardo, Davide 1
@article{AIF_2016__66_3_1217_0,
author = {Lombardo, Davide},
title = {On the $\ell $-adic {Galois} representations attached to nonsimple abelian varieties},
journal = {Annales de l'Institut Fourier},
pages = {1217--1245},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {3},
year = {2016},
doi = {10.5802/aif.3035},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3035/}
}
TY - JOUR AU - Lombardo, Davide TI - On the $\ell $-adic Galois representations attached to nonsimple abelian varieties JO - Annales de l'Institut Fourier PY - 2016 SP - 1217 EP - 1245 VL - 66 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3035/ DO - 10.5802/aif.3035 LA - en ID - AIF_2016__66_3_1217_0 ER -
%0 Journal Article %A Lombardo, Davide %T On the $\ell $-adic Galois representations attached to nonsimple abelian varieties %J Annales de l'Institut Fourier %D 2016 %P 1217-1245 %V 66 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3035/ %R 10.5802/aif.3035 %G en %F AIF_2016__66_3_1217_0
Lombardo, Davide. On the $\ell $-adic Galois representations attached to nonsimple abelian varieties. Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1217-1245. doi : 10.5802/aif.3035. https://aif.centre-mersenne.org/articles/10.5802/aif.3035/
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