Flach system on quaternionic Hilbert-Blumenthal surfaces and distinguished periods

Abstract 

In this talk, we will report some integrality result on the ratio of the quaternionic distinguished period associated to a Hilbert modular form and the quaternionic Petersson norm associated to a modular form. These distinguished periods are closely related to the notion of distinguished representations that play a prominent role in the proof of the Tate conjecture for Hilbert modular surfaces by Langlands-Rapoport-Harder. Our method is based on an Euler system argument initiated by Flach by producing elements in the motivic cohomologies of the quaternionic Hilbert–Blumenthal surfaces with control of their ramification behaviours. We show that these distinguished periods give natural bounds for certain subspaces of the Selmer groups of these quaternionic Hilbert–Blumenthal surfaces. The lengths of these subspaces can be determined by using the Taylor–Wiles method and can be related to the quaternionic Petersson norms of the modular forms.

About the speaker 

王海宁 复旦大学上海数学中心

2016年在谢明伦和李文卿的指导下获得宾夕法尼亚州立大学博士学位，随后在加拿大麦吉尔大学从事博士后工作，于2020年回国入职上海数学中心工作至今。

个人主页：

https://wanghaining11.github.io

BIMSA-YMSC Tsinghua

Number Theory Seminar

This is a research seminar on topics related to number theory and its applications which broadly can include related areas of interests such as analytic and algebraic number theory, algebra, combinatorics, algebraic and arithmetic geometry, cryptography, representation theory etc. The speakers are also encouraged to make their talk more accessible for graduate level students.

For more information, please refer to:

http://www.bimsa.cn/newsinfo/647938.html.