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

Benjamin Howard; Keerthi Madapusi

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arXiv · 2211.05108

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

Benjamin Howard·Keerthi Madapusi

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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.

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Benjamin Howard, Keerthi Madapusi. 2022-11-09. Kudla's modularity conjecture on integral models of orthogonal Shimura varieties. https://arxiv.org/abs/2211.05108

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