On Faltings heights of abelian varieties with complex multiplication
نویسندگان
چکیده
This expository article introduces some conjectures and theorems related to the Faltings heights of abelian varieties with complex multiplication. The topics include the Colmez conjecture, the averaged Colmez conjecture, and the André–Oort conjecture.
منابع مشابه
A fixed point formula of Lefschetz type in Arakelov geometry IV: the modular height of C.M. abelian varieties
We give a new proof of a slightly weaker form of a theorem of P. Colmez ([C2, Par. 2]). This theorem (Corollary 5.8) gives a formula for the Faltings height of abelian varieties with complex multiplication by a C.M. field whose Galois group over Q is abelian; it reduces to the formula of Chowla and Selberg in the case of elliptic curves. We show that the formula can be deduced from the arithmet...
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تاریخ انتشار 2017