The principle of functoriality
The principle of functoriality
复制标题
功能性原则
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
J. Arthur
中科院分区：
文献类型：
--
作者：
J. Arthur
根据组织者的明确指示，我试图写一篇适合一般数学观众的文章。它包含了一些类比和隐喻，甚至可以把非数学家。我希望专家们能容忍不可避免的简化。函数性原理是当今数学的中心问题之一。这是朗兰兹的一个意义深远但相当精确的猜想，它把基本的算术信息与同样基本的分析信息联系起来。算术信息来自代数方程的解。它包括分类代数数域和更一般的代数簇的数据。分析信息来自微分方程和群表示的谱。它包括对归约群的不可约表示进行分类的数据。
Following the explicit instructions of the organizers, I have tried to write an article that is suitable for a general mathematical audience. It contains some analogies and metaphors that might even be put to nonmathematicians. I hope that experts will be tolerant of the inevitable simplifications. The principle of functoriality is one of the central questions of present day mathematics. It is a far reaching, but quite precise, conjecture of Langlands that relates fundamental arithmetic information with equally fundamental analytic information. The arithmetic information arises from the solutions of algebraic equations. It includes data that classify algebraic number fields, and more general algebraic varieties. The analytic information arises from spectra of differential equations and group representations. It includes data that classify irreducible representations of reductive groups.