Elliptic Curves with Surjective Adelic Galois Representations
نویسنده
چکیده
Let K be a number field. The Gal(K/K)-action on the the torsion of an elliptic curve E/K gives rise to an adelic representation ρE : Gal(K/K) → GL2(Ẑ). From an analysis of maximal closed subgroups of GL2(Ẑ) we derive useful necessary and sufficient conditions for ρE 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.
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عنوان ژورنال:
- Experimental Mathematics
دوره 19 شماره
صفحات -
تاریخ انتشار 2010