{
  "abstract": "Let $V$ be a compact connected manifold and $G$ a simply connected solvable Lie group. We study $G$-Lie foliations on $V$ from the point of view of $\\mathcal{D}$-module theory, following the approach initiated by Dathe. To each singular foliation $\\mathcal{I}$, we associate the $\\mathcal{D}_X$-module $\\mathcal{M}_{\\mathcal{I}} = \\mathcal{D}_X / \\mathcal{D}_X \\cdot \\mathcal{I}$ and the derived ring $\\mathcal{D}_{\\mathcal{I}} := R\\mathcal{H}om_{\\mathcal{D}_X}(\\mathcal{M}_{\\mathcal{I}}, \\mathcal{M}_{\\mathcal{I}})$. We compute the D-irregularity $\\mathrm{D\\text{-}irr}(\\mathcal{I})$ for three classes of solvable Lie foliations: regular homogeneous foliations, the Meigniez foliation with non-polycyclic holonomy group, and an explicit foliation on a compact 5-dimensional manifold. We show that the non-polycyclicity of the holonomy group $Γ$ is reflected in the non-vanishing of higher cohomology groups of $\\mathcal{D}_{\\mathcal{I}}$, establishing a new connection between the geometry of the holonomy group and $\\mathcal{D}$-module invariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10583",
  "author_total": 1,
  "authors": [
    {
      "name": "Ameth Ndiaye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8zpcqp6z403pb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10583",
  "fulltext_url": null,
  "id": "8zpcqp6z403pb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10583",
  "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.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212259550",
  "pdf_url": "https://arxiv.org/pdf/2609.10583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8zpcqp6z403pb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "D-modules and Solvable Lie Foliations",
  "title_text": "D-modules and Solvable Lie Foliations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/8zpcqp6z403pb",
  "venue": "arXiv",
  "versions": []
}