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2010 Elliptic Curves with Surjective Adelic Galois Representations
Aaron Greicius
Experiment. Math. 19(4): 495-507 (2010).

Abstract

Let $K$ be a number field. The $\operatorname{Gal}(\bar{K}/K)$-action on the torsion of an elliptic curve $E/K$ gives rise to an adelic representation $ρ_E: \operatorname{Gal}(\bar{K}/K) \to \mathrm{GL}_2(\hat{\mathbb{Z}})$. From an analysis of maximal closed subgroups of $\mathrm{GL}_2(\hat{\mathbb{Z}})$ we derive useful necessary and sufficient conditions for $ρ_E$ to be surjective. Using these conditions, we compute an example of a number field $K$ and an elliptic curve $E/K$ that admits a surjective adelic Galois representation.

Citation

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Aaron Greicius. "Elliptic Curves with Surjective Adelic Galois Representations." Experiment. Math. 19 (4) 495 - 507, 2010.

Information

Published: 2010
First available in Project Euclid: 4 October 2011

zbMATH: 1263.11062
MathSciNet: MR2778661

Rights: Copyright © 2010 A K Peters, Ltd.

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Vol.19 • No. 4 • 2010
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