{
  "abstract": "Let $T$ be the theory of the valued field of complex Laurent series $\\mathbb{C}(\\!(t)\\!)$ in the language of rings expanded by a constant for $t$ and by predicates for $n$-th powers. We introduce a $t$-adic analogue of Kochen's operator, namely $γ(x)=x/(1+tx^{2})$, and the associated Kochen ring $Λ_{L}$ of a field extension $L$ of a model $K$ of $T$. Our main result characterizes the field extensions of $K$ which embed into a model of $T$ (the formally $T$-adic} fields): $L$ is formally $T$-adic if and only if $1/t\\notinΛ_{L}$. As an application we prove a Nullstellensatz for $\\mathbb{C}(\\!(t)\\!)$: a polynomial $f\\in K[X_{1},\\dots,X_{n}]$ vanishes on the zero set of an ideal $I$ if and only if $f^{m}=\\sum_{i}ω_{i}f_{i}$ for some $m\\geqslant 1$, generators $f_{i}$ of $I$ and coefficients $ω_{i}$ in the ring $Λ_{K(X)}\\cdot K[X]$. We derive the resulting correspondence between $R$-ideals and algebraic sets, and we compare natural incarnations of the associated $T$-spectrum: prime ideals, morphisms into models of $T$, and the space of types of $T$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14417",
  "author_total": 2,
  "authors": [
    {
      "name": "Pablo Cubides Kovacsics"
    },
    {
      "name": "Sebastián Uribe Rincón"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffyhgd68yk6eq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14417",
  "fulltext_url": null,
  "id": "ffyhgd68yk6eq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14417",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7221767850",
  "pdf_url": "https://arxiv.org/pdf/2610.14417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffyhgd68yk6eq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "A Nullstellensatz for the field of complex Laurent series",
  "title_text": "A Nullstellensatz for the field of complex Laurent series",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ffyhgd68yk6eq",
  "venue": "arXiv",
  "versions": []
}