论文标题
算术水平提高了某些Quaternionic Unity Shimura品种
Arithmetic level raising for certain quaternionic unitary Shimura variety
论文作者
论文摘要
在本文中，我们证明了算术级别提高了符合度的四分之一学位的定理。该结果是朝着与正交组相关的某些兰金·塞尔伯格（Rankin-Selberg）动机迈向贝林森 - 布洛赫 - 卡托（Beilinson-Bloch-kato）猜想的关键步骤。该定理本身也可以看作是Ihara引理的类似物，也可以看作是在经过分支特征下的Shimura品种特殊纤维的泰特猜想。证明在很大程度上取决于对某些Quaternionic Unity Shimura品种的超大轨迹的描述，这些shimura品种与经典的Siegel三倍密切相关。
In this article we prove an arithmetic level raising theorem for the symplectic group of degree four in the ramified case. This result is a key step towards the Beilinson-Bloch-Kato conjecture for certain Rankin-Selberg motives associated to orthogonal groups within the framework of the Gan-Gross-Prasad conjecture. The theorem itself can be also viewed as an analogue of the Ihara's lemma or the Tate conjecture for special fibers of Shimura varieties at ramified characteristics. The proof relies heavily on the description of the supersingular locus of certain quaternionic unitary Shimura variety which is closely related to the classical Siegel threefold.
