scholarly journals Abelian Varieties over Q and Modular Forms

2004 ◽  
pp. 241-261 ◽  
Author(s):  
Kenneth A. Ribet
Keyword(s):  
Modular Forms ◽  
Abelian Varieties

The Chowla–Selberg Formula and The Colmez Conjecture

2010 ◽  
Vol 62 (2) ◽  
pp. 456-472 ◽  
Author(s):  
Tonghai Yang
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Abelian Varieties ◽  
Siegel Modular Forms ◽  
Abelian Surface ◽  
Intersection Numbers ◽  
Abelian Surfaces ◽  
Elliptic Modular Form ◽  
Faltings Height

AbstractIn 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.

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