论文标题
椭圆形曲线和汤普森的零星简单组
Elliptic curves and Thompson's sporadic simple group
论文作者
论文摘要
我们表征了汤普森零星简单组的所有无限尺寸分级虚拟模块，其分级痕迹是重量3/2弱塑形模块化形式，满足了某些特殊特性。然后，我们使用这些模块来检测Mordell，Weil，Selmer和Tate--shafarevich的非平凡性，这是某些椭圆形曲线的二次曲折。
We characterize all infinite-dimensional graded virtual modules for Thompson's sporadic simple group, whose graded traces are weight 3/2 weakly holomorphic modular forms satisfying certain special properties. We then use these modules to detect the non-triviality of Mordell--Weil, Selmer, and Tate--Shafarevich groups of quadratic twists of certain elliptic curves.
