Álvaro Lozano-Robledo : $\ell$-adic Galois representations attached to elliptic curves with CM

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

At

March 11, 2022, 1 p.m.

In

Zoom

Abstract

In a recent preprint, Rouse, Sutherland, and Zureick-Brown have given a (conjectural) explicit classification of all the $\ell$-adic Galois representations (up to conjugation) attached to elliptic curves over $\mathbb{Q}$ without complex multiplication. In this talk, we apply a recent classification (by the speaker) of Galois representations attached to curves with CM to give a complete and explicit classification of all the $\ell$-adic Galois representations in the CM case over $\mathbb{Q}$. In particular, we will describe how many different representations appear for each rational j-invariant with CM.

Zoom link: https://uic.zoom.us/j/88173268700?pwd=aEhmTGpSOVhidWE4L1VWUnNhNVlvUT09 Meeting ID: 881 7326 8700 Passcode: 0t198j41