Résume | We report on joint work with T. Yang. Westudy the Faltings height pairing of arithmetic Heegner divisors and CM cycles on Shimura varieties associated to orthogonal groups. We compute the archimedean contributionto the height pairing and derive a conjecture relating the total pairingto the central derivative of a Rankin $L$-function. We briefly discusshow the conjecture can be proved in certain low dimensional cases.In particular, it can be used to give a new proof of the Gross-Zagierformula. |