On the -adic Galois representations attached to nonsimple abelian varieties
Annales de l'Institut Fourier, Volume 66 (2016) no. 3, p. 1217-1245

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).

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).

Received : 2015-03-30
Revised : 2015-09-11
Accepted : 2015-10-09
Published online : 2016-12-14
DOI : https://doi.org/10.5802/aif.3035
Classification:  11G10,  14K15,  11F80
Keywords: Tate classes, Hodge group, Galois representations, abelian varieties, Mumford-Tate conjecture
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {3},
     year = {2016},
     pages = {1217-1245},
     doi = {10.5802/aif.3035},
     language = {en},
     url = {http://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, Volume 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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