Kudla's modularity conjecture on integral models of orthogonal Shimura varieties

2022/11/09 by Howard, Benjamin, Madapusi, Keerthi
#11F46 (Secondary) #11G18 (Primary) 14G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2211.05108

Abstract

We construct a family of special cycle classes on the regular integral model of an orthogonal Shimura variety, and show that these cycle classes appear as Fourier coefficients of a Siegel modular form. Passing to the generic fiber of the Shimura variety recovers a result of Bruinier and Raum, originally conjectured by Kudla.

Related

• Derived special cycles on Shimura varieties
• Some cases of Kudla's modularity conjecture for unitary Shimura varieties
• Kudla's Modularity Conjecture and Formal Fourier-Jacobi Series
• Arithmetic special cycles and Jacobi forms
• The cohomological Kudla conjecture for unitary Shimura varieties