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. Andreatta
Primo
;
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.
Complex Multiplication, Faltings height, Shimura varieties, abelian varieties
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
mar-2018
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/544356
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