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arXiv · 0807.4954

Serre's uniformity problem in the split Cartan case

Yuri Bilu·Pierre Parent
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Abstract

We prove that there exists an integer p_0 such that X_split(p)(Q) is made of cusps and CM-points for any prime p>p_0. Equivalently, for any non-CM elliptic curve E over Q and any prime p>p_0 the image of the Galois representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an old question of Serre.

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Yuri Bilu, Pierre Parent. 2009-03-03. Serre's uniformity problem in the split Cartan case. https://arxiv.org/abs/0807.4954

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