局部单位方程与渐近费马最后定理。

Local criteria for the unit equation and the asymptotic Fermat's Last Theorem.

机构信息

Departament de Matemàtiques i Informàtica, Universitat de Barcelona, 08007 Barcelona, Spain.

Sorbonne Université, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS-Paris Diderot, 75005 Paris, France.

出版信息

Proc Natl Acad Sci U S A. 2021 Mar 23;118(12). doi: 10.1073/pnas.2026449118.

DOI:10.1073/pnas.2026449118

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8000273/

Abstract

Let F be a totally real number field of odd degree. We prove several purely local criteria for the asymptotic Fermat's Last Theorem to hold over F and also, for the nonexistence of solutions to the unit equation over F. For example, if two totally ramifies and three splits completely in F, then the asymptotic Fermat's Last Theorem holds over F.

摘要

设 F 为奇数次的实完全数域。我们证明了若干纯粹局部的条件，使得 Fermat 最后定理在 F 上成立，同时也使得 F 上单位方程无解。例如，如果两个分支完全分支，三个完全分裂，那么渐近 Fermat 最后定理在 F 上成立。

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