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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… Click to show full 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.
Keywords:
signature types;
conjecture;
colmez conjecture;
types unitary;
unitary colmez
Journal Title: Comptes Rendus Mathematique
Year Published: 2018
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Journal Title: Comptes Rendus Mathematique
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!