{
  "abstract": "In this largely expository article we give an introduction to higher dimensional local class field theory, more precisely class field theory for smooth projective schemes over local fields. We begin with a quick summary of some of the main results of classical local class field theory. Then we explain the main definitions and statements in the higher dimensional setting. We give a new and simple proof of the $\\ell$-part, which is originally due to Jannsen--Saito and Forré. Inspired by this proof, we propose a conjecture which would imply the remaining open cases with $p$-coefficients and which improves our understanding of the $p$-part. A particular goal of the exposition is to outline analogies between the classical and the higher dimensional theory and on how the unit filtration and ramification, i.e. the $p$- and the $\\ell$-part, can be interpreted in the higher dimensional setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34437",
  "author_total": 1,
  "authors": [
    {
      "name": "Morten Lüders"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kbjz3cpgtqhd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34437",
  "fulltext_url": null,
  "id": "1kbjz3cpgtqhd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34437",
  "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.AG"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214717763",
  "pdf_url": "https://arxiv.org/pdf/2609.34437",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kbjz3cpgtqhd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34437",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34437"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Higher dimensional local class field theory",
  "title_text": "Higher dimensional local class field theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1kbjz3cpgtqhd",
  "venue": "arXiv",
  "versions": []
}