Number Theory Seminar
Nathan Jones
UIC
Entanglements of division fields and applications
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.
Friday March 3, 2023 at 12:00 PM in 427 SEO