{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07173",
  "author_total": 3,
  "authors": [
    {
      "name": "Tony Feng"
    },
    {
      "name": "Zhiwei Yun"
    },
    {
      "name": "Wei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxz8pkyakdwva.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07173",
  "fulltext_url": null,
  "id": "cxz8pkyakdwva",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07173",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7202111795",
  "pdf_url": "https://arxiv.org/pdf/2608.07173",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxz8pkyakdwva.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.07173",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07173"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Modularity of Higher Theta Series III: Proof of the Modularity Conjecture",
  "title_text": "Modularity of Higher Theta Series III: Proof of the Modularity Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/cxz8pkyakdwva",
  "venue": "arXiv",
  "versions": []
}