The Chowla–Selberg Formula and The Colmez Conjecture

Yang, Tonghai

Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 456-472

Résumé

In this paper, we reinterpret the Colmez conjecture on the Faltings height of $\text{CM}$ abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a $\text{CM}$ abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for $\text{CM}$ abelian surfaces is equivalent to the cuspidality of this modular form.

Détail

DOI : 10.4153/CJM-2010-028-x

Mots-clés : 11G15, 11F41, 14K22

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