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arXiv · 2507.13299

The cohomological Kudla conjecture for unitary Shimura varieties

François Greer·Salim Tayou
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Abstract

We construct natural extensions of the Kudla--Millson generating series of cohomology classes of special cycles in compactified unitary Shimura varieties of signature $(n+1,1)$ and prove that they are holomorphic Hermitian modular forms. This proves the cohomological version of a conjecture of Kudla and Bruinier--Rosu--Zemel, in all codimensions up to the middle. We also develop the theory of Hermitian quasi-modular forms, with a particular focus on polynomial weighted theta functions, and prove that the generating series of Zariski closures of special cycles is a Hermitian quasi-modular form.

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François Greer, Salim Tayou. 2025-07-17. The cohomological Kudla conjecture for unitary Shimura varieties. https://arxiv.org/abs/2507.13299

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