Faltings heights of CM cycles and derivatives of L-functions

Details Faltings heights of CM cycles and derivatives of L-functions Faltings heights of CM cycles and derivatives of L-functions

2008-07-03

arxiv.org/abs/0807.0502v1

Mathematics

Number Theory

50 pages

Scientific paper

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.

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