论文标题
四季度订单的最佳旋转选择性
Optimal spinor selectivity for quaternion orders
论文作者
论文摘要
让$ d $为数字字段$ f $的四元基因代数，而$ \ mathscr {g} $是$ o_f $的任意属 - $ d $中的全等级。令$ k $是嵌入$ d $的$ f $的二次场扩展，而$ b $是$ o_f $ - $ k $中的$ o_f $ order，可以将其最佳地嵌入$ \ mathscr {g} $的某些成员中。我们为$ b $提供了必要和充分的条件，可以为$ \ mathscr {g} $最佳地选择性选择性，该属性概括了先前现有的现有的最佳选择性标准，该标准是由Arenas，Arenas-Carmona和Contreras给出的Eichler订单，以及由Voight独立的。这使我们能够获得最佳嵌入的经典痕迹公式的改进，该公式将称为旋转痕迹公式。当$ \ mathscr {g} $是Eichler订单的属时，我们将Maclachlan的相对导体公式扩展为从无方级别的Eichler订单中的最佳选择性到所有Eichler订单。
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 to obtain a refinement of the classical trace formula for optimal embeddings, which will be called the spinor trace formula. When $\mathscr{G}$ is a genus of Eichler orders, we extend Maclachlan's relative conductor formula for optimal selectivity from Eichler orders of square-free levels to all Eichler orders.
