abstract: Colmez conjectured an explicit formula for the height of CM abelian varieties in terms of special values of L functions. Recently Jacob Tsimerman showed that a weak form of Colmez conjecture would imply Andre'-Oort's conjecture without the GRH. I will present recent work of myself, Eyal Goren, Ben Howard and Keerthi Madapusi Pera providing a proof of this weak form of Colmez conjecture.