Insufficiency of the étale Brauer-Manin obstruction: towards a simply connected example

Arne Smeets

Since Poonen's construction of a variety $X$ defined over a number field $k$ for which $X(k)$ is empty and the étale Brauer--Manin set $X({\mathbf{A}}_k{)}^{\text{Br,et}}$ is not, severa…