欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
学术信息
SEMINARS
Rational points on complete symmetric hypersurfaces
时间  Datetime
2019-12-27 15:00 — 16:30 
地点  Venue
813
报告人  Speaker
Daqing Wan
单位  Affiliation
University of California, Irvine
邀请人  Host
Jiyou Li
报告摘要  Abstract

A basic problem in arithmetic geometry is to determine if a hypersurface of degree d over the finite field F_q of q elements has a non-trivial F_q-rational point. When the degree d is very small compared to the field size q (and the hypersurface is smooth), then Deligne's bound (Riemann hypothesis) settles this problem. When the degree d is large, this problem becomes out of reach in general. In this talk, we show that there are many F_q-rational points for complete symmetric hypersurfaces of dimension at least two, even for large degree d. This depends crucially on a coding theory result of Cheng-Li-Zhuang on deep holes of Reed-Solomon codes. This is a joint work with Jun Zhang.