发表机构
Research Institute for Mathematical Sciences, Kyoto University（京都大学数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文给出非阿基米德局部域上局部ε因子的朗兰兹第一主引理的完整局部证明，以Dwork的p进计算等为基础，还将完成第二主引理的Lean验证，助力实现朗兰兹设想的局部ε因子局部构造的完整证明。
AI 中文摘要
我们给出了非阿基米德局部域上局部ε因子的朗兰兹第一主引理的完整局部证明。该证明以Dwork的p进计算和朗兰兹的局部方法表述为基础，本文将这些计算在统一的正规化下重新表述，并将论证扩展到等特征情形。对平稳参数和导体情形的更系统处理旨在使计算更易于理解，范数-迹校正公式实现了等特征扩展。作者还在完成朗兰兹第二主引理的局部证明，并将在Lean中验证它。结合本文结果与朗兰兹的剩余归约，该工作将给出朗兰兹所设想的局部ε因子局部构造的完整证明。OpenAI ChatGPT协助了本文稿的起草和措辞修订；作者审核了文稿、检查了证明，并承担全部责任。
英文摘要
We give a complete local proof of Langlands's First Main Lemma for local epsilon factors over nonarchimedean local fields. The proof builds on Dwork's $p$-adic calculations and Langlands's formulation of the local method. The present paper reformulates these calculations in a common normalization and extends the argument to equal characteristic. A more systematic treatment of stationary parameters and conductor cases is intended to make the calculations easier to follow. 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 local epsilon factors envisioned by Langlands. OpenAI ChatGPT assisted with drafting and wording revisions of this manuscript; the author audited the manuscript, checked the proof, and assumes full responsibility.
CommentsCompanion to arXiv:2609.13960 and arXiv:2609.30301. The First Main Lemma proved here is used in the Second Main Lemma and its Lean formalization
