CM-Points on Straight Lines
  We prove that, with "obvious" exceptions, a CM-point (j(\tau),j(\tau')) cannot belong to a straight line in C^2 defined over Q. This generalizes a result of K\"uhne, who proved this for the line x+y=1. 
Bill Allombert, Yuri Bilu, Amalia Pizarro-Madariaga
math.NT