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We study the Selmer varieties of smooth projective curves of genus at least two defined over   $\mathbb{Q}$   which geometrically dominate a curve with CM Jacobian. We extend a result of Coates and Kim to show that Kim’s non-abelian Chabauty method applies to such a curve. By combining this with results of Bogomolov–Tschinkel and Poonen on unramified correspondences, we deduce that any cover of  P   $^1$   with solvable Galois group, and in particular any superelliptic curve over   $\mathbb{Q}$  , has only finitely many rational points over   $\mathbb{Q}$  .

Rational Points on Solvable Curves over ℚ via Non-Abelian Chabauty