Number Theory Seminar
Nathan Jones
UIC
Entanglements associated to elliptic curves
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 H. Daniels, and also with K. Vissuet and with S.M. Lee.
Join Zoom Meeting
https://uic.zoom.us/j/88173268700?pwd=aEhmTGpSOVhidWE4L1VWUnNhNVlvUT09
Meeting ID: 881 7326 8700
Passcode: 0t198j41
Friday January 28, 2022 at 1:00 PM in Zoom