Kolyvagin derivatives of modular points on elliptic curves

Hatton, Richard

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.

Citation

Hatton, R. (2021). Kolyvagin derivatives of modular points on elliptic curves. Journal of Number Theory, 229, 405-431. https://doi.org/10.1016/j.jnt.2020.10.014

• Journal Article Type: Article
• Acceptance Date: Oct 13, 2020
• Online Publication Date: Dec 30, 2020
• Publication Date: Dec 1, 2021
• Deposit Date: Jan 6, 2021
• Publicly Available Date: Dec 31, 2021
• Journal: Journal of Number Theory
• Print ISSN: 0022-314X
• Electronic ISSN: 1096-1658
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 229
• Pages: 405-431
• DOI: https://doi.org/10.1016/j.jnt.2020.10.014
• Keywords: Algebra and Number Theory
• Public URL: https://nottingham-repository.worktribe.com/output/5203405
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022314X20303498?