{
  "abstract": "Let $R$ be a normal $F$-finite ring of characteristic $p>0$. We show that one effective $\\mathbb{Q}$-divisor $Δ$, with $K_R+Δ$ $\\mathbb{Q}$-Cartier of index prime to $p$, computes the big test ideal. This answers a question of Schwede and Smith. More generally, we prove their conjecture that test module of a Cartier algebra acting on an ideal is the test module of a single map $ψ$ in the algebra and even the image of $ψ$. We prove a global version for schemes quasi-projective over an $F$-finite local ring as well. In particular, every such normal, locally strongly $F$-regular scheme admits an effective boundary $Δ$ for which $(X,Δ)$ is locally strongly $F$-regular and $K_X+Δ$ is $\\mathbb{Q}$-Cartier of index prime to $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38163",
  "author_total": 2,
  "authors": [
    {
      "name": "Rahul Ajit"
    },
    {
      "name": "with Appendix joint with Daniel Apsley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9egacc3q664f8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38163",
  "fulltext_url": null,
  "id": "9egacc3q664f8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38163",
  "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"
    ],
    [
      "arxiv",
      "math.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38163",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9egacc3q664f8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38163",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38163"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Test ideals can be computed by boundaries",
  "title_text": "Test ideals can be computed by boundaries",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9egacc3q664f8",
  "venue": "arXiv",
  "versions": []
}