Eichler序、树和表示域
Eichler orders, trees and Representation Fields
摘要：
若H和D是中心单代数A中的两个阶，且D是最大秩的，则表示域F（D| H）是D的亏格的旋量类域的一个子域，它决定了该亏格中代表H阶的阶的旋量亏格的集合。以前的工作主要集中在两种情况，极大序模D和交换序H。在这项工作中，我们展示了如何计算表示场F（D| H）当D是一个有限的极大序模族的交集时，例如，一个Eichler阶，H是任意的。提供了实例。
英文摘要：
If H and D are two orders in a central simple algebra A with D of maximal rank, the representation field F(D|H) is a subfield of the spinor class field of the genus of D which determines the set of spinor genera of orders in that genus representing the order H. Previous work have focused on two cases, maximal orders D and commutative orders H. In this work, we show how to compute the representation field F(D|H) when D is the intersection of a finite family of maximal orders, e.g., an Eichler order, and H is arbitrary. Examples are provided.
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