Some Contemporary Problems with Origins in the Jugendtraum
Some Contemporary Problems with Origins in the Jugendtraum
复制标题
一些当代问题的根源在于青年时代
DOI：
10.1090/pspum/028.2/0437500
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发表时间：
2001
影响因子：
0.8
通讯作者：
R. Langlands
中科院分区：
文献类型：
--
作者：
R. Langlands
希尔伯特的第十二个问题提醒我们，虽然提醒应该是不必要的，三个主题的血缘关系，因为经历了往往单独的发展。其中第一个理论，即类域理论或数域的阿贝尔扩张理论，在本世纪早期就达到了它的最后形式。第二个是椭圆曲线的代数理论，更一般地说，是阿贝尔簇的代数理论，五十年来一直是一个研究主题，其活力和质量尚未显示出减弱的迹象。第三，理论的自守函数，已缓慢成熟，仍然是无法摆脱纠缠的研究阿贝尔品种，特别是他们的模。
The twelfth problem of Hilbert reminds us, although the reminder should be unnecessary, of the blood relationship of three subjects which have since undergone often separate developments. The first of these, the theory of class fields or of abelian extensions of number fields, attained what was pretty much its final form early in this century. The second, the algebraic theory of elliptic curves and, more generally, of abelian varieties, has been for fifty years a topic of research whose vigor and quality shows as yet no sign of abatement. The third, the theory of automorphic functions, has been slower to mature and is still inextricably entangled with the study of abelian varieties, especially of their moduli.