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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Geometric Langlands correspondence ： ウィキペディア英語版 Geometric Langlands correspondence In mathematics, the geometric Langlands correspondence is a geometric reformulation of the classical Langlands correspondence from number theory. ==Overview== In mathematics, the classical Langlands correspondence is a collection of results and conjectures relating number theory to the branch of mathematics known as representation theory. Formulated by Robert Langlands in the late 1960s, the Langlands correspondence is related to important conjectures in number theory such as the Taniyama-Shimura conjecture, which includes Fermat's last theorem as a special case.〔Frenkel 2007, p. 3〕 In spite of its importance in number theory, establishing the Langlands correspondence in the number theoretic context has proved extremely difficult. As a result, some mathematicians have worked on a related conjecture, the geometric Langlands correspondence. This is a geometric reformulation of the classical Langlands correspondence which is obtained by replacing the number fields appearing in the original version by function fields and applying techniques from algebraic geometry.〔 In a paper from 2007, Anton Kapustin and Edward Witten described a connection between the geometric Langlands correspondence and S-duality, a property of certain quantum field theories.〔Kapustin and Witten 2007〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Geometric Langlands correspondence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.