This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus of modular curves to all Shimura varieties given by totally indefinite quaternion algebras over totally real number fields. Second, we generalize the result of Ribet on arithmetic level raising to such Shimura varieties in the inert case. Third, as an application to number theory, we use the previous results to study the Selmer group of certain triple product motive of an elliptic curve, in the context of the Bloch--Kato conjecture.

中文翻译：

---

Hilbert 模变体、算术水平提升和 Selmer 群的超奇异轨迹

这篇文章有三个目标。首先，我们将 Deuring 和 Serre 关于模曲线的超奇异轨迹表征的结果推广到由完全不定四元数代数在完全实数域上给出的所有 Shimura 变体。其次，我们将 Ribet 在算术水平提升上的结果推广到惰性情况下的此类 Shimura 变体。第三，作为对数论的应用，我们在Bloch--Kato猜想的背景下，利用前面的结果来研究椭圆曲线的某些三重乘积动机的Selmer群。