Geodesic
The Chowla–Selberg Formula and The Colmez Conjecture
Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 456-472

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DOI

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.
DOI : 10.4153/CJM-2010-028-x
Mots-clés : 11G15, 11F41, 14K22 
Yang, Tonghai. The Chowla–Selberg Formula and The Colmez Conjecture. Canadian journal of mathematics, Tome 62 (2010) no. 2, pp. 456-472. doi: 10.4153/CJM-2010-028-x
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     title = {The {Chowla{\textendash}Selberg} {Formula} and {The} {Colmez} {Conjecture}},
     journal = {Canadian journal of mathematics},
     pages = {456--472},
     year = {2010},
     volume = {62},
     number = {2},
     doi = {10.4153/CJM-2010-028-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-028-x/}
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