论文标题
在Shimura曲线和总库德拉（Kudla）的三重产品上提高算术水平 - 旋转对角线循环II：两部分Euler System
Arithmetic level raising on triple product of Shimura curves and Gross--Kudla--Schoen Diagonal cycles II: Bipartite Euler system
论文作者
论文摘要
在本文中，我们研究了Shimura曲线在一个良好降低的位置的三重产物上的总孔 - 切成角度周期，并证明了该三重产物共同体学定理的毫无疑问的算术水平。我们从中推断出一种互惠定律，该定律将亚伯 - 雅各比（Jacobi）映射下对角线周期的图像与库德拉类型的某些时期积分相关联。将其与我们先前一项工作证明的第一条互惠法梳理，我们表明，kudla- schoen-choen-Choen-Choen循环形成了一个两部分欧拉系统，用于对称立方体的模块化形式的动机。作为一种应用，我们为模块化形式的对称立方体动机的Bloch-Kato猜想的等级提供了一些证据。
In this article, we study the Gross--Kudla--Schoen diagonal cycle on the triple product of Shimura curves at a place of good reduction and prove an unramified arithmetic level raising theorem for the cohomology of this triple product. We deduce from it a reciprocity law which relates the image of the diagonal cycle under the Abel--Jacobi map to certain period integral of Gross--Kudla type. Combing this with the first reciprocity law we proved in a previous work, we show that the Gross--Kudla--Schoen diagonal cycles form a bipartite Euler system for the symmetric cube motive of a modular form. As an application we provide some evidence for the rank one case of the Bloch--Kato conjecture for the symmetric cube motive of a modular form.
