Lang-Trotter Phenomena and Unlikely Intersections

I will discuss how the Lang–Trotter conjecture for pairs of elliptic curves implies new cases of the Zilber–Pink conjecture for curves in 3. Unlike previous results for curves in 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.