Faltings heights of CM cycles and derivatives of L-functions

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We study the Faltings height pairing of arithmetic Heegner divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedian contribution to the height pairing and derive a conjecture relating the total pairing to the central derivative of a Rankin L-function. We prove the conjecture in certain cases where the Shimura variety has dimension 0, 1, or 2. In particular, we obtain a new proof of the Gross-Zagier formula.
50 pages

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Number Theory, Algebraic Geometry, 11G18, 14G40, 11F67

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http://salesiana.dossiersoluciones.com/handle/123456789/164130

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.0502
 http://arxiv.org/abs/0807.0502

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arXiv