  We extend the work of S. Zhang and Yuan-Zhang-Zhang to obtain a Gross-Zagier
formula for modular forms of even weight in terms of an arithmetic intersection
pairing of CM-cycles on Kuga-Sato varieties over Shimura curves. Combined with
a result of the first author and de Vera-Piquero adapting Kolyvagin's method of
Euler systems to this setting, we bound the associated Selmer and
Tate-Shafarevich groups, assuming the non-vanishing of the derivative of the
L-function at the central point.
