Counting Points on Modular Curves over Finite Fields
Student No.:40
Time:Tue & Fri 08:00-09:35, Sep.18-Dec.14
Instructor:陈宗彬Chen Zongbin  
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-9-18
Ending Date:2018-12-14

We will explain the Langlands-Kottwitz approach to counting points on modular curves over finite fields. Firstly, we will explain the reduction of modular curves over finite fields. Secondly, we will explain the Arthur-Selberg trace formula. Combining them, we will explain how to express the zeta function of modular curves in terms of modular forms. If time permits, we will explain how to elaborate these calculations to deduce local Langlands correspondence for GL_2(Q_p).

Prerequisite: Basic notions of algebraic geometry and representation theory

[1] Katz, Mazur: Arithmetic moduli of elliptic curves;
[2] Langlands, Modular forms and l-adic representations;
[3] Scholze, The Langlands-Kottwitz approach for modular curves;
[4] Deligne, Letter to Piatetski-Shapiro.