Coding the real locus of X_0+(N)

$\boldsymbol{\rm GU}(2,n-2)$型志村簇的超奇异轨迹

The supersingular locus of the Shimura variety of $\mathrm{GU}(2,n-2)$

该研究聚焦$\rm GU(2,n-2)$型志村簇惰性素数约化的超奇异轨迹，将其不可约分支表为Deligne–Lusztig簇上旗概形的完满化显式条件闭子概形，并借助Frobenius幂分层刻画分支相交性质。

Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups

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.

$p$-进伴随 $L$-函数与 Hilbert 模特征簇的分歧轨迹

A $p$-adic adjoint $L$-function and the ramification locus of the Hilbert modular eigenvariety

本文研究了全实域上 Hilbert 模特征簇的分歧轨迹与伴随 $L$-值 $p$-进性质的关系，通过解析扭曲 Poincaré 配对和 $L$-理想理论建立联系，推广了 $F=\mathbb{Q}$ 的情形。

阿特金多项式用于具有实乘法的阿贝尔簇族

Atkin polynomials for families of abelian varieties with real multiplication

本文通过正交多项式与帕德逼近的关系，研究了具有实乘法的阿贝尔簇族的非普通域几何，并应用超几何恒等式确定了阿特金多项式的递推关系。