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The Chowla–Selberg Formula and The Colmez Conjecture

Published online by Cambridge University Press:  20 November 2018

Tonghai Yang
Tonghai Yang*
Affiliation:
Department of Mathematics, University of Wisconsin Madison, Madison, WI 53706, USA, e-mail: thyang@math.wisc.edu
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Abstract

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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.

Keywords

11G1511F4114K22
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 2 , 01 April 2010 , pp. 456 - 472
Copyright
Copyright © Canadian Mathematical Society 2010

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