Primes of cyclic reduction for elliptic curves

Abstract: Given an elliptic curve E over a number field F and a prime of good reduction p, the group of rational points on the reduced curve E mod p is abelian on at most two generators. If one generator suffices, we call p a prime of cyclic reduction for E. In this talk I will explain why the set of primes of cyclic reduction for E should have a natural density and I will discuss the possible vanishing of this density. This is a joint work with Peter Stevenhagen.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October