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.

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

1 Institut für Algebra, Zahlentheorie und Diskrete Mathematik Universität Hannover Welfengarten 1, 30165 Hannover, Germany
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Davide Lombardo. 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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.970/

[1] Davide Lombardo Bounds for Serre’s open image theorem for elliptic curves over number fields, Algebra Number Theory, Volume 9 (2015) no. 10, pp. 2347-2395 | Article

[2] Davide Lombardo An explicit open image theorem for products of elliptic curves, J. Number Theory, Volume 168 (2016), pp. 386-412 | Article

[3] David William Masser; Gisbert Wüstholz Galois properties of division fields of elliptic curves, Bull. Lond. Math. Soc., Volume 25 (1993) no. 3, pp. 247-254 | Article

[4] Richard Pink Classification of pro-p subgroups of SL 2 over a p-adic ring, where p is an odd prime, Compos. Math., Volume 88 (1993) no. 3, pp. 251-264

[5] Kenneth A. Ribet Galois action on division points of Abelian varieties with real multiplications, Am. J. Math., Volume 98 (1976), pp. 751-804 | Article

[6] Jean-Pierre Serre Abelian -adic Representations and Elliptic Curves, Research Notes in Mathematics, A. K. Peters/CRC Press, 1997, 208 pages

[7] Luqun Wang Automorphisms of 2-dimensional linear groups over a local rings, J. Math. Res. Expo., Volume 5 (1985) no. 1, pp. 25-28

[8] Siman Wong Twists of Galois representations and projective automorphisms, J. Number Theory, Volume 74 (1999) no. 1, pp. 1-18 | Article

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