The Frobenius twists of elliptic curves over global function fields

TL;DR

This paper investigates how the p-Selmer group size of an elliptic curve over a global function field increases after applying the Frobenius twist, highlighting a notable phenomenon in positive characteristic settings.

Contribution

It provides a discussion on the tendency of the p-Selmer group of Frobenius twists of elliptic curves to grow larger, elucidating this behavior over global function fields.

Findings

p-Selmer groups of Frobenius twists tend to be larger

The phenomenon occurs specifically in characteristic p>0

The paper discusses the underlying reasons for this growth

Abstract

For an elliptic curve A defined over a global function field K of characteristic p>0, the p-Selmer group of the Frobenius twist of A tends to have larger order than that of A. The aim of this note is to discuss this phenomenon.