Pink-type results for general subgroups of SL 2 ( ) n
Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 85-127.

We study open subgroups G of SL 2 ( ) n in terms of some associated Lie algebras without assuming that G is a pro- group, thereby extending a theorem of Pink. The result has applications to the study of families of Galois representations.

Nous étudions les sous-groupes ouverts G de SL 2 ( ) n en termes de certaines algèbres de Lie, et ceci sans supposer que G est un groupe pro-. Le résultat étend un théorème dû à Pink et a des applications à l’étude de certaines familles de représentations galoisiennes.

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DOI: 10.5802/jtnb.970
Classification: 20E18, 11E95, 11E57, 20F40, 20G25
Keywords: Lie algebras, profinite groups, special linear group, $p$-adic integers
Lombardo, Davide 1

1 Institut für Algebra, Zahlentheorie und Diskrete Mathematik Universität Hannover Welfengarten 1, 30165 Hannover, Germany
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     journal = {Journal de th\'eorie des nombres de Bordeaux},
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Lombardo, Davide. Pink-type results for general subgroups of $\operatorname{SL}_2(\mathbb{Z}_\ell )^n$. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 85-127. doi : 10.5802/jtnb.970. http://archive.numdam.org/articles/10.5802/jtnb.970/

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