Self-points on elliptic curves

Some remarks on self-points on elliptic curves

“…with the perspective to study the rank of the E(L) in some infinite Iwasawa extensions L. A special case of these points are the so-called "self-points" in the title. They were defined and have also been investigated in [DW09] and [Wut09].…”

“…Note that there are #P 1 (Z/N Z) cyclic subgroups, C ⊂ E, of order N . The question of the rank generated by the self-points (and also by the "higher" self-points) has been studied in generality in [Wut09]. One of the key ingredient is to determine when the point P C is a non-torsion point.…”

Kolyvagin derivatives of modular points on elliptic curves

“…Proof. The following has been adapted from the proof of [13,Theorem 2] for the more general setting. Let p be a prime which divides the denominator of the j-invariant of A.…”

“…In this paper, we use these points to bound Selmer groups using methods similar to that of Kolyvagin in [10] and Wuthrich in [13]. Kolyvagin initially looked at a specific type of modular point known as Heegner points and used them to bound Selmer groups.…”

“…We then follow a similar method to Wuthrich in [13] from the ideas of Kolyvagin in [10]. We create derivative classes coming from higher modular points of infinite order which are not divisible by p in E(Q(C)) as shown in Proposition 2.4.…”