Inventiones mathematicae

, Volume 177, Issue 3, pp 631–681

Faltings heights of CM cycles and derivatives of L-functions


DOI: 10.1007/s00222-009-0192-8

Cite this article as:
Bruinier, J.H. & Yang, T. Invent. math. (2009) 177: 631. doi:10.1007/s00222-009-0192-8


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 

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of MathematicsUniversity of Wisconsin MadisonMadisonUSA

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