{
  "abstract": "We give a complete characterization of the weak Lefschetz property (WLP) for monomial complete intersections over a field of positive characteristic. Richard Stanley observed that in characteristic zero WLP, and in fact the strong Lefschetz property (SLP), holds for all degree sequences, as a consequence of the hard Lefschetz theorem, and the same result was explained by Junzo Watanabe using the representation theory of $\\mathfrak{sl}_2$. In positive characteristic, many partial results are known, most notably the classification for constant degree sequences due to Brenner--Kaid and Kustin--Vraciu. Our approach is based on a cohomological and representation-theoretic interpretation of WLP. Combined with an analysis of cohomology characters, this leads to a complete numerical criterion for WLP, expressed by simple inequalities involving the $p$-adic digits of the exponents. We also give a new proof of the known classification of SLP using Renaud's algorithm for multiplication in the Green--Han--Monsky ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09534",
  "author_total": 4,
  "authors": [
    {
      "name": "Annet Kyomuhangi"
    },
    {
      "name": "Emanuela Marangone"
    },
    {
      "name": "Claudiu Raicu"
    },
    {
      "name": "Ethan Reed"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/32rda20pxc7np.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09534",
  "fulltext_url": null,
  "id": "32rda20pxc7np",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09534",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212125764",
  "pdf_url": "https://arxiv.org/pdf/2609.09534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/32rda20pxc7np.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lefschetz properties for monomial complete intersections",
  "title_text": "Lefschetz properties for monomial complete intersections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/32rda20pxc7np",
  "venue": "arXiv",
  "versions": []
}