Inventiones mathematicae

, Volume 177, Issue 3, pp 631-681

Faltings heights of CM cycles and derivatives of L-functions

  • Jan Hendrik BruinierAffiliated withFachbereich Mathematik, Technische Universität Darmstadt Email author 
  • , Tonghai YangAffiliated withDepartment of Mathematics, University of Wisconsin Madison

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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.

Mathematics Subject Classification (2000)

14G40 11G18 11F67