论文标题
Heegner循环在Shimura曲线和Selmer组上的不可分割性
Indivisibility of Heegner cycles over Shimura curves and Selmer groups
论文作者
论文摘要
在本文中，我们表明，Heegner的Abel-Jacobi图像在Nekovar，Besser和Chida-hsieh构建的Shimura曲线上循环，Chida-hsieh在Howard的意义上形成了双方的Euler系统。作为此应用，我们推断出与较高的重量模块化的Gross-Zagier-kolyvagin型定理的相反，以推广Wei Zhang and Skinner的作品，以使重量的模块化形式二。也就是说，我们表明，如果某些残留Selmer组的等级是一个，则Heegner循环的Abel-Jacobi图像在残留Selmer组中不是零。
In this article, we show that the Abel-Jacobi images of the Heegner cycles over the Shimura curves constructed by Nekovar, Besser and the theta elements contructed by Chida-Hsieh form a bipartite Euler system in the sense of Howard. As an application of this, we deduce a converse to Gross-Zagier-Kolyvagin type theorem for higher weight modular forms generalizing works of Wei Zhang and Skinner for modular forms of weight two. That is, we show that if the rank of certain residual Selmer group is one, then the Abel-Jacobi image of the Heegner cycle is non-zero in the residual Selmer group.
