Special cycles on unitary Shimura varieties II: Global theory

We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature. (n - 1, 1). We define arithmetic cycles on these models and study their intersection behavior. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s = 0 of a certain incoherent Eisenstein series for the group U(n, n). This is done by relating the arithmetic cycles to their formal counterpart from part I [33] via non-archimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of part I and a counting argument.