Title:Independence of CM points in Elliptic curves.

Abstract: (Joint with Jonathan Pila) Let Y be a shimura curve and E an elliptic curve. Consider a map f:Y→ E. It is a theorem of Poonen and Buium that the images of CM points in E are - mostly - linearly independent. We explain this, and a generalization of this theorem to correspondences, via a connection to unlikely intersection theory. Our proof follows the by-now-familiar setup of combining transcendence theorems with Galois orbit bounds, and employs the full strength of the Ax-Schanuel theorem.