# Special cycles on unitary Shimura varieties II: global theory

@article{Kudla2009SpecialCO,
title={Special cycles on unitary Shimura varieties II: global theory},
author={Stephen S. Kudla and Michael Rapoport},
journal={arXiv: Algebraic Geometry},
year={2009}
}
• Published 18 December 2009
• Mathematics
• arXiv: Algebraic Geometry
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… Expand
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