.png){kind=icon}
返回
Pariah moonshine
.png){kind=icon}
OA
AI
DOI：10.1038/s41467-017-00660-y.png)
.png){kind=icon}
.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate-Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.
Keyword:
ELLIPTIC-CURVES
MONSTER
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
15.7
论文数:
9.3W
被引数:
91.2W
机构
引用论文
Neurons lying in the white matter of the upper cervical spinal cord project to the intermediolateral cell column.png)
Neuroscience
NeuroscienceIF0
PREAI
分享收藏
查看更多内容