{
  "abstract": "We introduce level structures on tropical abelian varieties and give a modular interpretation of $A_g[m]^{\\mathrm{trop}}$, the tropicalization of the moduli space $\\mathcal{A}_g[m]$ of principally polarized abelian varieties with level $m$ structure. We study the case of abelian surfaces in greater depth. The link of $A_2[m]^{\\mathrm{trop}}$ is an explicit simplicial complex whose vertices are the primitive vectors of $(\\mathbb{Z}/m\\mathbb{Z})^4$ up to sign. As a topological space, this link is homotopic to a wedge sum of closed orientable surfaces and circles; we compute the number of each of these and the genera of the surfaces. We deduce the weight zero compactly supported rational cohomology of $\\mathcal{A}_2[m]$, completing a calculation of Oda-Schwermer from 1990.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14895",
  "author_total": 5,
  "authors": [
    {
      "name": "Eran Assaf"
    },
    {
      "name": "Madeline Brandt"
    },
    {
      "name": "Juliette Bruce"
    },
    {
      "name": "Melody Chan"
    },
    {
      "name": "Raluca Vlad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxckgbvr8346a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14895",
  "fulltext_url": null,
  "id": "bxckgbvr8346a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14895",
  "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",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213316000",
  "pdf_url": "https://arxiv.org/pdf/2609.14895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxckgbvr8346a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Level structures on tropical abelian varieties",
  "title_text": "Level structures on tropical abelian varieties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bxckgbvr8346a",
  "venue": "arXiv",
  "versions": []
}