Elliptic curves over ℚ $\mathbb {Q}$ and 2-adic images of Galois
By Jeremy A. Rouse, David Zureick-Brown. 2014
55 citations recorded by the source corpus.
AbstractWe give a classification of all possible 2-adic images of Galois representations associated to elliptic curves over ℚ $\mathbb {Q}$ . To this end, we compute the ‘arithmetically maximal’ tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/80269a58b0995ba50eb54bdb4603511f3bde8d44
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Galois representations attached to elliptic curves with complex multiplication (2018, methodology): “For instance, Rouse and Zureick-Brown have classified the possible 2-adic images for non-CM curves (see [17]), and Sutherland and Zywina have produced a conjectural list of all the possible mod p images ([24], [27]) which is complete if we assume a positive answer to a uniformity question of Serre.”