Article

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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Abstract

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