Heights and L-series
Student No.:40
Time:Tue&Thu, 15:20-16:55
Instructor:Cai Li  
Place:Conference Room 1,Jin Chun Yuan West Bldg.
Starting Date:2019-2-25
Ending Date:2019-5-17

In this course, we shall discuss the relation of heights and L-series. Firstly, we will introduce the height function as an important tool for counting points (starting from Fermat’s infinite descent method). Then we will discuss about the Neron-Tate height pairing on Jacobians of curves, which can be decomposed into local heights. The famous work of Gross and Zagier relates the Neron-Tate heights of Heegner points with (derivative) center value of certain Rankin-Selberg L-series. We shall discuss about its proof and applications to the B-SD conjecture. Finally, we will introduce recent generalizations of the Gross-Zagier formula.