Elliptic curves attached to abelian threefolds with imaginary multiplicationMPIM

by Pip Andrew Goodman (MPIM)

Wednesday Oct 21, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

Let A be an abelian threefold defined over a number field K whose geometric endomorphism algebra is isomorphic to an imaginary quadratic field M. In recent joint work with Fité, under mild assumptions on K, we proved the existence of an elliptic curve E defined over K with CM by M such that for any prime \ell, the twisted Tate module V_\ell(E)(1) is a subrepresentation of \wedge^3 V_\ell(A).

In this talk I will give an overview of the proof of the above result, families of examples of such abelian threefolds and the corresponding elliptic curves. Depending on time, I might also talk about their residual respresentations.