Kolyvagin derivatives of modular points on elliptic curves

[摘要] Let E/Q and A/Q be elliptic curves. We can construct mod-ular 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 par-ticular, using Kolyvagin's construction of derivative classes, we can find elements in certain Shafarevich-Tate groups of order p(n). (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Elliptic curve;Modular point;Modular curve;Selmer group