Special Fibers of Shimura Curves and Special Representations
报告题目(Title)：Special Fibers of Shimura Curves and Special Representations
报告人(Speaker)：余屹正 (台湾政治大学应用数学系)
地点(Place)：电子楼105教室
时间(Time)：2019年4月25日, 14:30 - 15:30
邀请人(Inviter)：胡维
报告摘要
One of the monumental examples of Langlands program is the Jacquet-Langlands correspondence which is a correspondence between automorphic forms on GL(2) and its twisted forms. The correspondence between division algebras of dimension n^2 and GL(n) was proved by Jacquet and Langlands in both the local and global settings, hence the name. In 1983, Rogawski extended the local Jacquet-Langlands correspondence to division algebras of higher dimension in characteristic 0. Deligne, Kazhdan and Vigneras carried out the case of a general inner form of GL(n,F) in characteristic 0 in 1984, and Badulescu in characteristic pp in 2002. Each of these cases was accomplished by embedding the local problem into a global one and then applying Selberg trace formula methods. In this talk, we study the geometry of the special fibers of certain Shimura curves and give a direct proof of global-to-local Jacquet-Langlands compactibility by Cerednik-Drinfeld uniformizations theorem.
