Time：15:00-16:00, Thursday, May 8 2025
Venue：E4-233
Speaker：Jiangwei Xue, Wuhan University
Title：Refined class-type number formulas of totally definite quaternion orders and selectivity
Abstract：The notion "selectivity" is first introduced by Chinburg and Friedman in 1999 to describe the phenomenon that certain quadratic orders tend to embed into some but not all maximal orders in a fixed indefinite quaternion algebra, as if they have selected some maximal order to embed into. This theory was further developed by Chan and Xu, Guo and Qin, and many others. However, most of the development focus on the indefinite case (i.e., when the quaternion algebra satisfies the Eichler condition). In this talk, we explain the generalization of the selectivity theory to the totally definite case and then apply it to obtain several refined class/type number formulas for totally definite quaternion orders. Such formulas enable us to prove certain divisibility results about these class/type numbers. This talk is based on joint works with Yucui Lin and Chia-Fu Yu.
