Generating series of intersection volumes of special cycles on unitary Shimura varieties

2017/10/16 by Amir-Khosravi, Zavosh
#11F27 #11F30 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1710.05580

Abstract

We form a generating series of regularized volumes of intersections of special cycles on a non-compact unitary Shimura variety with a fixed base change cycle. We show that it is a Hilbert modular form by identifying it with a theta integral, which we show converges even though the parameters lie outside the classical convergence range of Weil. By applying the regularized Siegel-Weil formulas of Ichino and Gan-Qiu-Takeda, we show the modular form is the restriction of a hermitian modular form of degree n related to Siegel Eisenstein series on U(n,n). An essential fact used is a computation showing the Kudla-Millson Schwartz function vanishes under the Ikeda map.

Related

• Special cycles on unitary Shimura varieties II: global theory
• Derived special cycles on Shimura varieties
• Intersections of special cycles on the Shimura variety for GU(1,2)
• Arithmetic special cycles and Jacobi forms
• Special cycles on unitary Shimura varieties with minuscule parahoric level structure