Kolyvagin derivatives of modular points on elliptic curves

Abstract

Let E/Q and A/Q be elliptic curves. We can construct modular points derived from A via the modular parametrisation of E. With certain assumptions we can show that these points are of infinite order and are not divisible by a prime p. In particular, using Kolyvagin's construction of derivative classes, we can find elements in certain Shafarevich-Tate groups of order pn.