3 0 Ju l 2 00 8 Serre ’ s Uniformity in the Split Cartan Case
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چکیده
We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of the Galois representation ρE,p 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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5 A ug 2 00 8 Serre ’ s Uniformity Problem in the Split Cartan Case
We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of the representation of Gal(¯ Q/Q) 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 ol...
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