On the independence of Heegner points in the function field case
Journal
Journal of Number Theory
Journal Volume
130
Journal Issue
11
Pages
2542-2560
Date Issued
2010
Author(s)
Wei, F.-T.
Abstract
Let ∞ be a fixed place of a global function field k. Let E be an elliptic curve defined over k which has split multiplicative reduction at ∞ and fix a modular parametrization ΦE:X0(Tsh{cyrillic})→E. Let P1,...,Pr∈E(k{topbar}) be Heegner points associated to the rings of integers of distinct quadratic "imaginary" fields K1,...,Kr over (k,∞). We prove that if the "prime-to-2. p" part of the ideal class numbers of ring of integers of K1,...,Kr are larger than a constant C=C(E,ΦE) depending only on E and ΦE, then the points P1,...,Pr are independent in E(k{topbar})/Etors. Moreover, when k is rational, we show that there are infinitely many imaginary quadratic fields for which the prime-to-2. p part of the class numbers are larger than C. © 2010 Elsevier Inc.
Type
journal article