四元数代数上斜埃尔米特型的旋量范

Optimal spinor selectivity for quaternion Bass orders

Let $A$ be a quaternion algebra over a number field $F$, and $\mathcal{O}$ be an $O_F$-order of full rank in $A$. Let $K$ be a quadratic field extension of $F$ that embeds into $A$, and $B$ be an $O_F$-order in $K$. Suppose that $\mathcal{O}$ is a Bass order that is well-behaved at all the dyadic primes of $F$. We provide a necessary and sufficient condition for $B$ to be optimally spinor selective for the genus of $\mathcal{O}$. This partially generalizes previous results on optimal (spinor) selectivity by C. Maclachlan [Optimal embeddings in quaternion algebras. J. Number Theory, 128(10):285…

Optimal spinor selectivity for quaternion orders

Let $D$ be a quaternion algebra over a number field $F$, and $\mathscr{G}$ be an arbitrary genus of $O_F$-orders of full rank in $D$. Let $K$ be a quadratic field extension of $F$ that embeds into $D$, and $B$ be an $O_F$-order in $K$ that can be optimally embedded into some member of $\mathscr{G}$. We provide a necessary and sufficient condition for $B$ to be optimally spinor selective for the genus $\mathscr{G}$, which generalizes previous existing optimal selectivity criterions for Eichler orders as given by Arenas, Arenas-Carmona and Contreras, and by Voight independently. This allows us t…

关于四元数酉群的志村簇超奇异轨迹

On the supersingular locus of Shimura varieties for quaternionic unitary groups

本文研究全实域上全不定四元数代数中斜埃尔米特形式所对应的酉相似群志村簇，给出了斜埃尔米特自对偶格存在的充要条件，证明了超特殊轨迹非空，并在p为奇数且非分歧时给出超奇异轨迹不可约分量数的显式公式。

完全确定四元数代数的旋量类型数公式

The spinor type number formula for totally definite quaternion orders

本文研究了完全确定四元数代数的旋量类型数公式，证明了类型数可被相关商群阶整除，并扩展了类数可被类数整除的结果。

关于规范原理的旋量群的赫尔曼引理

Hensel's lemma for the norm principle for spinor groups

本文在规范原理成立的条件下，证明了旋量群的赫尔曼引理在四元数代数上的有效性。

全定四元数代数范数一群的迹公式

Trace formulas for the norm one group of totally definite quaternion algebras

该研究将Eichler、Pizer关于全定四元数代数Eichler序的迹公式相关结果拓展至范数一群，提出剩余非分歧序下的类数公式及旋子类理想类数公式，引入辅助不变量并借助最优旋子选择性理论构建公式。