An Effective Version of Chevalley-Weil Theorem for Projective Plane Curves
نویسندگان
چکیده
We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let φ : C̃ → C be an unramified morphism of non-singular plane projective curves defined over a number field K. We calculate an effective upper bound for the norm of the relative discriminant of the number field K(Q) over K for any point P ∈ C(K) and Q ∈ φ(P ). 2000 MCS: 14G25, 14H25, 11G30.
منابع مشابه
Supplementary Lecture Notes on Elliptic Curves
1. What is an elliptic curve? 2 2. Mordell-Weil Groups 5 2.1. The Group Law on a Smooth, Plane Cubic Curve 5 2.2. Reminders on Commutative Groups 8 2.3. Some Elementary Results on Mordell-Weil Groups 9 2.4. The Mordell-Weil Theorem 11 2.5. K-Analytic Lie Groups 13 3. Background on Algebraic Varieties 15 3.1. Affine Varieties 15 3.2. Projective Varieties 18 3.3. Homogeneous Nullstellensätze 20 3...
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