{
  "abstract": "Let $\\mathcal O$ be the Lubin--Tate deformation ring of a one-dimensional commutative formal group of finite height $n\\geq1$ over a perfect field $k$ of characteristic $p$. We identify Rezk's Witt filtration $\\{I_d\\}$ with the divisibility filtration of integral trace pairings on subgroup algebras of fixed source lifts. This gives the geometric recursion \\[ I_{d+1}=pI_d+J_{d,z}\\qquad(d\\geq0), \\] where $J_{d,z}$ defines the targets of order-$p^d$ quotient isogenies from a $W(k)$-valued lift $z$ of the closed point. The corrected ideal is independent of $z$. We also compute the cokernel of the universal source trace pairing over $\\mathcal O$: it is $\\bigoplus_{j=1}^d(\\mathcal O/p^j)^{r_j-r_{j-1}}$, where $r_j$ counts order-$p^j$ subgroups of $(\\mathbf Q_p/\\mathbf Z_p)^n$. The same duality extends the generic trace along two-step isogeny flags to an integral surjection, even when the flag-forgetting map is not flat. This computes composition in the subring of weighted trace operations. Applications include sharp projector denominators and congruence fibre products for full-torsion loci.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18246",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Taccani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6c3vqk6ng1q1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18246",
  "fulltext_url": null,
  "id": "c6c3vqk6ng1q1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18246",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221811325",
  "pdf_url": "https://arxiv.org/pdf/2610.18246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6c3vqk6ng1q1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.18246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Integral trace duality and the Witt filtration on Lubin--Tate space",
  "title_text": "Integral trace duality and the Witt filtration on Lubin--Tate space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/c6c3vqk6ng1q1",
  "venue": "arXiv",
  "versions": []
}