Program
Seminar Number Theory
Student No.:40
Time:Mon 15:20-16:55, Oct.08-Jan.14
Instructor:Fu Lei, Xu Bin, Cai Li, Chen Zongbin, Chun-Yin Hui, Wang Haoran, Li Yongxiong, Liu Yu  
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-10-8
Ending Date:2019-1-14

2018-12-10

Place: Jing Zhai 105

Speaker: Sarah Dijols (YMSC, Tsinghua University)

Title: The Generalized Injectivity Conjecture

Abstract:
The Generalized Injectivity Conjecture of Casselman-Shahidi states that the unique irreducible generic subquotient of a (generic) standard module is necessarily a subrepresentation. It is related to $L$-functions, as studied by Shahidi, hence has some number-theoretical flavor, although our technics lie in the fields of representations of reductive groups over local fields. It was proven for classical groups (SO(2n+1), Sp(2n), SO(2n)) by M.Hanzer in 2010. In this talk, I will first explain our interest in this conjecture, and describe its main ingredients. I will further present our proof (under some restrictions) which uses techniques more amenable to prove this conjecture for all quasi-split groups.


2018-11-26

Speaker: Jilong Tong (Capital Normal University)

Title: Comparison theorems in p-adic Hodge theory

Abstract:
In the first part of my talk, I shall review some definitions of Scholze's pro-etale site and his proof of de Rham comparison theorem for rigid analytic spaces. Then, I shall concentrate in crystalline comparison theorems: I will introduce the so-called pro-etale crystalline topos, and sketch the proof of a version of crystalline comparison theorem, generalizing a previous result of Faltings. This part is based on a joint work with Yichao Tian.


2018-11-19

Speaker: Emmanuel Lecouturier (YMSC, Tsinghua)

Title: Application of a conjecture of Mazur-Tate to the supersingular elliptic curves


2018-11-12

Speaker: Jinzhao Pan (YMSC, Tsinghua)

Title: The full BSD conjecture for a CM elliptic curve of analytic rank one at a supersingular prime (II)

Abstract:
Let $E$ be a CM elliptic curve defined over rational numbers with analytic rank one. The full BSD conjecture for $E$ at a good supersingular prime is proved by Kobayashi, based on previous works by Gross-Zagier, Rubin, Kolyvagin, Perrin-Riou, et al. In the first talk I'll briefly introduce these works and some key ingredients in them, and the comparison to my work at a potentially supersingular prime joint with Ye Tian. In this second talk some more technical details will be concerned.


2018-11-5

Speaker: Jinzhao Pan (Yau MSC, Tsinghua)

Title: The full BSD conjecture for a CM elliptic curve of analytic rank one at a supersingular prime (I)

Abstract:
Let $E$ be a CM elliptic curve defined over rational numbers with analytic rank one. The full BSD conjecture for $E$ at a good supersingular prime is proved by Kobayashi, based on previous works by Gross-Zagier, Rubin, Kolyvagin, Perrin-Riou, et al. In the first talk I'll briefly introduce these works and some key ingredients in them, and the comparison to my work at a potentially supersingular prime joint with Ye Tian. In the second talk some more technical details will be concerned.


2018-10-22

Speaker: Xu Shen (Morningside center, CAS)

Title: p-adic period domains and the Fargues-Rapoport conjecture

Abstract:
In his 1970 ICM report, Grothendieck asked the question to describe the p-adic analogues of Griffiths period domains. In this talk, we will review some constructions for these p-adic period domains, following recent developments in p-adic Hodge theory. We will then explain some ideas in a proof of the Fargues-Rapoport conjecture about the structure of certain p-adic period domains. This is joint work with Miaofen Chen and Laurent Fargues.


2018-10-15

Speaker: Xin Wan (Morningside center, CAS)

Title: Iwasawa theory and BSD formula for GL(2)

Abstract:
We first give an overview of recent results on Iwasawa theory and applications to BSD formulas for elliptic modular forms. Then we explain some ingredients used for the argument.


2018-10-08

Speaker: Xinyi Yuan [U. C. Berkeley & IAS Tsinghua]

Title: Modular heights of Shimura curves

Abstract:
In this talk, I will introduce a formula expressing the modular height of a quaternionic Shimura curve over a totally real field in terms of the logarithmic derivative at 2 of the Dedekind zeta function of the totally real field. The proof of the formula is inspired by the previous work of Yuan-Zhang-Zhang on the Gross-Zagier formula.