  The canonical height associated to a polarized endomporhism of a projective
variety, constructed by Call and Silverman and generalizing the N\'eron-Tate
height on a polarized Abelian variety, plays an important role in the
arithmetic theory of dynamical systems. We generalize this construction to
polarized correspondences, prove various fundamental properties, and show how
the global canonical height decomposes as an integral of a local height over
the space of absolute values on the algebraic closure of the field of
definition.
