|Date: Friday, March 11, 2022
Location: 2866 East Hall (3:00 PM to 4:00 PM)
Title: Brauer-Manin Obstruction
Abstract: It is a classical question to ask whether a system of polynomial equations with rational coefficients has a rational solution. One promising approach is to look for solutions over all completions of Q and try to put these together to give a solution over Q. This is called a local-to-global principle. However, this reconstruction notably fails in general and hence it is difficult to determine whether rational points exist. In this talk we will introduce some of these phenomena and define the Brauer-Manin obstruction, which, in certain cases, is able to detect the failure of the local-to-global principle. Time permitting, we will consider a surface (due to Iskovskikh) over the rationals where the failure of local-to-global can be seen by computing the Brauer-Manin obstruction.
Speaker: Zheng Yang