Special cycles on unitary Shimura varieties II: global theory

2009/12/18 by Kudla, Stephen, Rapoport, Michael · 2 citations
#14G35 11F15 11F18 11F27 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0912.3758

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.

Cited by

• The cohomological Kudla conjecture for unitary Shimura varieties
• Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups

Related

• Intersections of special cycles on the Shimura variety for GU(1,2)
• On Shimura varieties for unitary groups
• Generating series of intersection volumes of special cycles on unitary Shimura varieties
• Arithmetic diagonal cycles on unitary Shimura varieties
• Derived special cycles on Shimura varieties