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Faltings heights of CM cycles and derivatives of L-functions

2009; Springer Science+Business Media; Volume: 177; Issue: 3 Linguagem: Inglês

10.1007/s00222-009-0192-8

1432-1297

Jan Hendrik Bruinier, Tonghai Yang,

Analytic Number Theory Research

We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the Archimedean 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.