A Uniform Bound for Rational Points on Twists of a given Curve
نویسنده
چکیده
THEOREM 1. Let K/Q be a number field, and let C/K be a smooth projective curve of genus at least 2. For each^class ^ e i / 1 (Gal (AT/AT), Aut(C)), let C% be the twist of C by x (cf. [11, X §3]) and le\Jx = J ac (Q be the Jacobian variety of Cx. There is a constant y = y{C/K) such that #C,( /Q^r7 a n k * ( K ) forallxeH{G2\{K/K),A\xi{C)). We illustrate this general theorem by applying it to a particular class of curves, the Catalan curves. Compare the following result with [12], where a similar bound was proven for the integer points on these curves.
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