Special cycles on unitary Shimura varieties II: global theory
Abstract
We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature (n1, 1). We define arithmetic cycles on these models and study their intersection behaviour. In particular, in the nondegenerate 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 nonarchimedean 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2009
 arXiv:
 arXiv:0912.3758
 Bibcode:
 2009arXiv0912.3758K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G35 11F15 11F18 11F27
 EPrint:
 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