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Kudla constructed a family of special cycles on canonical models of orthogonal Shimura varieties, and conjectured that they are the Fourier coefficients of a Siegel modular form valued in the Chow group.  This conjecture was proved by Bruinier and Raum.  I will explain how to extend this modularity result from canonical models to canonical integral models.  This is joint work with Keerthi Madapusi.

ES Program Research Seminar: Modularity Of Generating Series Of Cycles On Orthogonal Shimura Varieties