# Smallness of Faltings heights of CM abelian varieties

@inproceedings{Wei2021SmallnessOF, title={Smallness of Faltings heights of CM abelian varieties}, author={Xunjing Wei}, year={2021} }

We prove that assuming the Colmez conjecture and the “no Siegel zeros” conjecture, the stable Faltings height of a CM abelian variety over a number field is less than or equal to the logarithm of the root discriminant of the field of definition of the abelian variety times an effective constant depending only on the dimension of the abelian variety. In view of the fact that the Colmez conjecture for abelian CM fields, the averaged Colmez conjecture, and the “no Siegel zeros” conjecture for CM…

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