{
  "abstract": "We study two invariants measuring the asymptotic abundance of surjections between modules. We prove that Hashimoto's asymptotic surjective number is attained over local rings, hence it is a rational number. We also prove that its associated function is constructible in families and on spectra; on the latter, it is moreover lower semicontinuous on the support of the target. We establish the existence of the F-surjective signature, a common generalization of F-signature and dual F-signature, and prove that it is superadditive in its source and varies lower semicontinuously across the spectrum under mild assumptions. As applications, we obtain new rationality results for dual F-signature and prove a transformation inequality under finite maps, with consequences for quotient singularities and reduction mod p.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22104",
  "author_total": 2,
  "authors": [
    {
      "name": "Ilya Smirnov"
    },
    {
      "name": "Kevin Tucker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d85sbdmcf7652.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22104",
  "fulltext_url": null,
  "id": "d85sbdmcf7652",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22104",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7222509645",
  "pdf_url": "https://arxiv.org/pdf/2610.22104",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d85sbdmcf7652.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22104",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22104"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The asymptotic surjective number and F-surjective signature",
  "title_text": "The asymptotic surjective number and F-surjective signature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/d85sbdmcf7652",
  "venue": "arXiv",
  "versions": []
}