  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.
