Conference abstracts

Session S13 - Number Theory

July 26, 17:30 ~ 18:00

## CM-points on straight lines

### Amalia Pizarro Madariaga

### Universidad de Valparaíso, Chile - amalia.pizarro@uv.cl

A CM-point (or special point) is a point of the form $(j(\tau_1),j(\tau_2))$ where both $\tau_1,\tau_2$ are imaginary quadratic numbers. In this talk we will show that, with ”obvious” exceptions, a CM-point cannot belong to a straight line in $\mathbb{C}^2$ defined over $\mathbb{Q}$.

Joint work with Bill Allombert (Université de Bordeaux) and Yuri Bilu (Université de Bordeaux).