Rational Points on Solvable Curves over ℚ via Non-Abelian Chabauty
نویسندگان
چکیده
We study the Selmer varieties of smooth projective curves genus at least two defined over $\mathbb{Q}$ which geometrically dominate a curve with CM Jacobian. extend result Coates and Kim to show that Kim's non-abelian Chabauty method applies such curve. By combining this results Bogomolov-Tschinkel Poonen on unramified correspondences, we deduce any cover $\mathbf{P}^1$ solvable Galois group, in particular superelliptic $\mathbb{Q}$, has only finitely many rational points $\mathbb{Q}$.
منابع مشابه
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2021
ISSN: ['1687-0247', '1073-7928']
DOI: https://doi.org/10.1093/imrn/rnab141