Special Year Learning Seminar

I will discuss how the Lang–Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber–Pink conjecture for curves in $\mathcal{A}_3$. Unlike previous results for curves in $\mathcal{A}_g$, our result does not rely on any assumption on intersections with the boundary, and in particular applies to compact curves. The argument is based on the $G$-functions method of Yves André.

This is based on joint work in progress with Chris Daw.