Kolyvagin’s descent and Mordell-Weil groups over ring class fields
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چکیده
whereX0(N) is the complete curve overQ which classifies pairs of elliptic curves related by a cyclic N -isogeny. The curve E is equipped with the collection of Heegner points defined over ring class fields of suitable imaginary quadratic fields. More precisely, let K be an imaginary quadratic field in which all rational primes dividing N are split and let O be the order of K of conductor c prime to N . There exists a proper O-ideal N such that the natural projection of complex tori C/O → C/N−1 (1)
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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تاریخ انتشار 2007