Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic space over Q of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain L-functions. As an application of this result, we prove an averaged version of Colmez’s conjecture on the Faltings heights of CM abelian varieties.
Faltings heights of abelian varieties with complex multiplication / F. Andreatta, E. Goren, B. Howard, K. Madapusi Pera. - In: ANNALS OF MATHEMATICS. - ISSN 0003-486X. - 187:2(2018 Mar), pp. 391-531. [10.4007/annals.2018.187.2.3]
Faltings heights of abelian varieties with complex multiplication
F. AndreattaPrimo
;
2018
Abstract
Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic space over Q of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain L-functions. As an application of this result, we prove an averaged version of Colmez’s conjecture on the Faltings heights of CM abelian varieties.
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