Fermat最后定理——历史和证明简介  

Fermat Last Theorem——A Brief on History and Proof

作　　者：张绍伟[1] 

机构地区：[1]北京大学数学系,100871

出　　处：《数学进展》1993年第6期502-507,共6页Advances in Mathematics（China）

摘　　要：本文旨在介绍Fermat最后定理的历史和Wiles最近所给的证明。首先简介了其在代数数论的发展过程中所起的作用,然后介绍椭圆曲线的基本概念,叙述Taniyama-Weil猜想,即任一椭圆曲线都是模的。进而介绍Ribet的工作,他证明了若Taniyama-Weil猜想对半稳定的椭圆曲线成立则Fermat最后定理成立。最后介绍l-adic Galois表示的概念及Wiles定理,即半稳定的椭圆曲线都是模的,从而这和Ribet的工作一起蕴含了Fermat最后定理。The aim of this paper is to sketch the history of Fermat last theorem and Wiles' proof for it. Firstly we describe its role in the devoloping of algebraic number theory. Secondly we introduce the basic concepts in the theory of elliptic curves. State the Taniyama-Weil conjecture, that is, every elliptic curve is modular. Thirdly we sketch Ribet's work, which says that Taniyama-Weil conjecture for semi-stable elliptic curves implies Fermat last theorem. Finally we give the definition of l-adic Galois representation and Wiles' theorem, which states that every semi-stable elliptic curve is modular, therefore together with Ribet's theorem it implies Fermat last theorem.

关 键 词：费马最后定理 T-W猜想 代数数论 

分 类 号：O156.2[理学—数学]