, Volume 177, Issue 3, pp 631-681

Faltings heights of CM cycles and derivatives of L-functions

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

The second author is partially supported by grants NSF DMS-0555503 and NSFC-10628103.