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 $f:Y\rightarrow E$. 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.

algebraic geometrynumber theory

Audience: researchers in the topic

MAGIC (Michigan - Arithmetic Geometry Initiative - Columbia)

Series comments: Description: Research seminar in arithmetic geometry

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