The Chowla–Selberg Formula and The Colmez Conjecture
نویسنده
چکیده
In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
منابع مشابه
Chowla-selberg Formula and Colmez’s Conjecture
In this paper, we reinterpret the Colmez conjecture on Faltings’ height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving Faltings’ height of a CM abelian surface and arithmetic intersection numbers, and prove that Colmez’s conjecture for CM abelian surfaces is equivalent to the cuspitality of this modular form.
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