# Special cycles on unitary Shimura varieties II: global theory

Stephen Kudla, Michael Rapoport

Number | 45 |
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Author | Michael Rapoport |

Project | B10 |

Year | 2009 |

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.