{
  "abstract": "We give a complete local proof of Langlands’s First Main Lemma for normalized one-dimensional local epsilon factors over every nonarchimedean local field, in both mixed and equal characteristic. The proof reconstructs and completes the local method initiated by Dwork and organized by Langlands; its decisive p-adic calculations and guiding ramification-theoretic and stationary-phase ideas are due to them. The present paper unifies their normalizations and supplies omitted endpoint and non-stable wild calculations. Exact norm–trace correction formulas yield the equal-characteristic extension. The author is also completing a local proof of Langlands’s Second Main Lemma and will verify it in Lean. Together with the present result and Langlands’s remaining reductions, that work will give a complete proof of the local construction of epsilon factors envisioned by Langlands, without global functional equations. Open AI ChatGPT assisted the drafting and English-language editing of this manuscript; the author audited the complete text, checked the proof against the completed Lean formalization, and assumes full responsibility.",
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  "article_type": null,
  "arxiv": "2610.10583",
  "author_total": 1,
  "authors": [
    {
      "name": "Fukuhiro Ueda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dedkc45krmpkr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10583",
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  "id": "dedkc45krmpkr",
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  "landing_url": "https://hal.science/hal-05735672v1",
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      "2610|Advanced Algebra and Geometry"
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  "pdf_url": "https://hal.science/hal-05735672/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
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  "ris": "https://research.draconitic.com/paper/dedkc45krmpkr.ris",
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      "first_seen": "2026-10-30T12:17:27Z",
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      "origin": "openalex:2610|Advanced Algebra and Geometry",
      "subfield": "mathematical-physics"
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  "title": "A LOCAL PROOF OF LANGLANDS'S FIRST MAIN LEMMA FOR LOCAL EPSILON FACTORS OVER NONARCHIMEDEAN LOCAL FIELDS",
  "title_text": "A LOCAL PROOF OF LANGLANDS'S FIRST MAIN LEMMA FOR LOCAL EPSILON FACTORS OVER NONARCHIMEDEAN LOCAL FIELDS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/dedkc45krmpkr",
  "venue": "HAL",
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}