Abstract:Colmez conjectured a formula relating the Faltings height of CM abelian varieties to a certain linear combination of log 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.2010 Mathematics Subject Classification. Primary: 11G15.
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