MASSEY PRODUCTS FOR ELLIPTIC CURVES OF RANK 1

摘要

The author must begin with an apology for writing on a topic so specific, so elementary, and so well-understood as the study of elliptic curves of rank 1. Nevrtheless, it is hoped that a contribution not entirely without value or novelty is to be found within the theory of Selmer varieties for hyperbolic curves, applied to the complement X = E {e} of the origin inside an elliptic curve E over Q with Mordell-Weil rank 1. Assume throughout this paper that p is an odd prime of good reduction such that III(E)[p1 is finite and that E has integral j-invariant. All of these assumptions will hold, for example, if E has complex multiplication and ord_s=~1L(E, s) = 1.