English

Kolyvagin Derivatives of Modular Points on Elliptic Curves

Number Theory 2021-01-08 v3

Abstract

Let E/QE / \mathbb{Q} and A/QA / \mathbb{Q} be elliptic curves. We can construct modular points derived from AA via the modular parametrisation of EE. With certain assumptions we can show that these points are of infinite order and are not divisible by a prime pp. In particular, using Kolyvagin's construction of derivative classes, we can find elements in certain Shafarevich-Tate groups of order pnp^{n}.

Keywords

Cite

@article{arxiv.1910.07335,
  title  = {Kolyvagin Derivatives of Modular Points on Elliptic Curves},
  author = {Richard Hatton},
  journal= {arXiv preprint arXiv:1910.07335},
  year   = {2021}
}

Comments

Final Version. To appear in Journal of Number Theory. 23 pages