On the -adic Galois representations attached to nonsimple abelian varieties  [ Sur les représentations galoisiennes associées aux variétés abéliennes non simples ]
Annales de l'Institut Fourier, Tome 66 (2016) no. 3, pp. 1217-1245.

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).

Reçu le : 2015-03-29
Révisé le : 2015-09-10
Accepté le : 2015-10-08
Publié le : 2016-12-13
DOI : https://doi.org/10.5802/aif.3035
Classification : 11G10,  14K15,  11F80
Mots clés : classes de Tate, groupe de Hodge, représentations de Galois, variétés abéliennes, conjecture de Mumford-Tate
@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'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     doi = {10.5802/aif.3035},
     language = {en},
     url = {www.numdam.org/item/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. http://www.numdam.org/item/AIF_2016__66_3_1217_0/

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