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PreprintCC BY-NC-ND 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{feng2026modularity,
  title = {{Modularity of Higher Theta Series III: Proof of the Modularity Conjecture}},
  author = {Tony Feng and Zhiwei Yun and Wei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.07173},
  eprint = {2608.07173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.07173},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Modularity of Higher Theta Series III: Proof of the Modularity Conjecture
AU  - Tony Feng
AU  - Zhiwei Yun
AU  - Wei Zhang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2608.07173
UR  - https://arxiv.org/abs/2608.07173
AB  - 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.
ER  -