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椭圆曲线与模块化

Elliptic curves and modularity
课程网址: https://videolectures.net/8ecm2021_thorne_elliptic_curve/  
主讲教师: Jack Thorne
开课单位: 8ECM会议
开课时间: 2021-07-06
课程语种: 英语
中文简介:
椭圆曲线的模性猜想最著名的是其有理数上椭圆曲线的公式——事实上,Wiles证明了半稳定椭圆曲线在有理数上的模性,这是他证明Fermat最后定理的一部分。最近,在更一般的数域上研究椭圆曲线的模性问题已经成为可能。我将解释这意味着什么,我们知道什么,以及我们对丢番图方程的解可以期待什么样的结果。
课程简介: The modularity conjecture for elliptic curves is most famous in its formulation for elliptic curves over the rational numbers – indeed, Wiles proved the modularity of semistable elliptic curves over the rationals as part of his proof of Fermat’s Last Theorem. Recently it has become possible to attack the problem of modularity of elliptic curves over more general number fields. I will explain what this means, what we know, and what kinds of consequences we can expect for the solution of Diophantine equations.
关 键 词: 椭圆曲线; Fermat最后定理; 模性问题
课程来源: 视频讲座网
数据采集: 2024-05-23:liyq
最后编审: 2024-05-23:liyq
阅读次数: 3