Signature (n − 2,2) CM types and the unitary Colmez conjecture

Abstract

Colmez conjectured a formula relating the Faltings height of CM abelian varieties to a certain linear combination of logarithmic derivatives of L-functions. In this paper, we study the case of unitary CM fields and by studying the class functions that arise, we reduce the conjecture to a special case. Using the Galois action, we prove more cases of the Colmez Conjecture.