On the asymptotic behaviour of Heegner points. (English) Zbl 0977.11025
The authors proved that there are only finite pairs \((D,f)\), where \(D\) is the discriminant of an imaginary quadratic number field and \(f\) the conductor of the corresponding ring class field \(\text{mod }f\) , \(K_f\) over \(K\), so that the order of the Heegner points on \(E(K_f)\) of an modular elliptic curve \(E\) defined over \(\mathbb Q\) is finite.
Reviewer: Jannis A. Antoniadis (Iraklion)
MSC:
11G15 | Complex multiplication and moduli of abelian varieties |
11G05 | Elliptic curves over global fields |
11G40 | \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture |
11R23 | Iwasawa theory |
11R34 | Galois cohomology |