{
  "abstract": "Using window theory, Bodzenta--Donovan showed that the derived category of a root stack $\\sqrt[n]{X/D}$ has a $2n$-periodic $2$-term semiorthogonal decomposition. We define a categorical generalization of the root stack construction and interpret this as a pullback on the B-side of the 3d mirror symmetry equivalence of Gammage--Hilburn--Mazel-Gee. We analyze this pullback using categorical representation theoretic results of Ben-Zvi--Francis--Nadler and Ben-Zvi--Nadler--Preygel applied to SODs. We also show that the pullback is equivalent to a pushforward of perverse schobers on the A-side, allowing us to deduce periodicity from a simple decomposition of an A-side Lagrangian skeleton. Additionally, we adapt the construction of Bodzenta--Donovan to a new GIT problem, which yields an embedding of Coh($\\sqrt[m]{X/D}$) into Coh($\\sqrt[n]{X/D}$) for $m<n$ coprime, and prove $2n$-periodicity of the resulting $2$-term SOD.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30350",
  "author_total": 3,
  "authors": [
    {
      "name": "Swapnil Garg"
    },
    {
      "name": "Ruoxi Li"
    },
    {
      "name": "Yuji Okitani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddgb3hsw52p96.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30350",
  "fulltext_url": null,
  "id": "ddgb3hsw52p96",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30350",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204954505",
  "pdf_url": "https://arxiv.org/pdf/2608.30350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddgb3hsw52p96.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "GIT for root stacks and 3d mirror symmetry",
  "title_text": "GIT for root stacks and 3d mirror symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ddgb3hsw52p96",
  "venue": "arXiv",
  "versions": []
}