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arXiv · 2608.07173

Modularity of Higher Theta Series III: Proof of the Modularity Conjecture

Tony Feng·Zhiwei Yun·Wei Zhang
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Abstract

We prove the Modularity Conjecture for higher theta series on moduli stacks of Hermitian shtukas. For general linear shtukas, we establish a more refined phenomenon that we call supermodularity. As a key input, we prove the Trace Conjecture for Hitchin stacks of low corank, realizing virtual fundamental classes of special cycles as categorical traces.

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Tony Feng, Zhiwei Yun, Wei Zhang. 2026-09-16. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture. https://arxiv.org/abs/2608.07173

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