Rational points on curves
نویسنده
چکیده
2 Faltings’ theorem 15 2.1 Prelude: the Shafarevich problem . . . . . . . . . . . . . . . . 15 2.2 First reduction: the Kodaira–Parshin trick . . . . . . . . . . . 17 2.3 Second reduction: passing to the jacobian . . . . . . . . . . . 19 2.4 Third reduction: passing to isogeny classes . . . . . . . . . . . 19 2.5 Fourth reduction: from isogeny classes to `-adic representations 21 2.6 The isogeny conjecture . . . . . . . . . . . . . . . . . . . . . . 24 2.7 The finiteness principle for rational `-adic representations . . . 26 2.8 A summary of Faltings’ proof . . . . . . . . . . . . . . . . . . 28
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