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 behaviour. 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 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.
- Pub Date:
- December 2009
- Mathematics - Algebraic Geometry;
- Mathematics - Number Theory;
- 14G35 11F15 11F18 11F27
- Material on occult period maps has been moved to a separate article. Various corrections and improvements in exposition have been made. Accepted for publication in Crelle