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Faltings heights of CM cycles and derivatives of L-functions

Authors
  • Bruinier, Jan Hendrik
  • Yang, Tonghai
Type
Preprint
Publication Date
Jul 03, 2008
Submission Date
Jul 03, 2008
Identifiers
arXiv ID: 0807.0502
Source
arXiv
License
Yellow
External links

Abstract

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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