Inventiones mathematicae

, Volume 177, Issue 3, pp 631–681 | Cite as

Faltings heights of CM cycles and derivatives of L-functions

Article

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 

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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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