Hasse Principle for the Lines on the Intersection of Two Quadrics over Global Function Fields
Time: 2026-10-13
Published By: He Liu
Speaker(s): Jie Xu (BICMR)
Time: 15:00-16:00 October 16, 2026
Venue: Room 77201, Jingchunyuan 78, BICMR
The Hasse principle asks whether a variety over a global field has a rational point whenever it has a point over every completion of that field. In this talk, we consider the Fano variety of lines of smooth intersection of two quadrics X and establish the Hasse principle for it \(F_1(X)\): if \(X\) contains a line over every completion of \(k\), then it contains a line defined over \(k\), where \(k\) is a global function field of odd characteristic. The main arithmetic inputs are Prof. Zhiyu Tian's theorems on the Hasse principle and weak approximation for intersections of two quadrics, together with his recent local–global theorem for quartic del Pezzo surfaces. I will explain the geometric construction and the additional argument required in the boundary case \(n=7\).
