Special cycles on unitary Shimura varieties II: global theory

Stephen Kudla; Michael Rapoport

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arXiv · 0912.3758

Special cycles on unitary Shimura varieties II: global theory

Stephen Kudla·Michael Rapoport

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Abstract

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.

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Stephen Kudla, Michael Rapoport. 2012-12-18. Special cycles on unitary Shimura varieties II: global theory. https://arxiv.org/abs/0912.3758

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