Faltings heights of CM cycles and derivatives of L-functions
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- Bruinier, J.H. & Yang, T. Invent. math. (2009) 177: 631. doi:10.1007/s00222-009-0192-8
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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.