Finite Coverings and Rational Points

نویسنده

  • Michael Stoll
چکیده

The purpose of this talk is to put forward a conjecture. The background is given by the following Basic Question. Given a (smooth projective) curve C over a number field k, can we determine explicitly the set C(k) of rational points? One possible approach to this is to consider an unramified covering D π → C that is geometrically Galois. By standard theory, there are only finitely many twists Dj πj → C of this covering (up to isomorphism over k) such that Dj has points everywhere locally, and C(k) = ∐

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تاریخ انتشار 2005