Nathan Jones : Entanglements of division fields and applications

Posted by Nathan Jones , part of the Number Theory Seminar.

At

March 3, 2023, noon

In

427 SEO

Abstract

Given an elliptic curve E over a number field K, we say that E has an entanglement if the intersection of two division fields of E of coprime level is larger than K. Mazur's Program B, which asks for a classification of the elliptic curves whose adelic Galois representation lands inside a given fixed open subgroup of the group of (finite) adelic points of GL2, falls naturally into two parts: first, to classify all of the p-adic images for each prime p; and second, to classify the entanglements. In this talk, I will discuss motivating examples and survey various recent results in this area, some of which are based on joint work of mine with K. McMurdy, and also with K. Vissuet and with S. M. Lee.