Rationality of A1-connected smooth proper varieties in higher dimensions

Determine whether every A1-connected smooth proper variety of dimension greater than two is rational.

Background

The paper establishes that a smooth proper A1-connected surface over an algebraically closed field of characteristic zero is rational. It also notes that A1-connectedness implies vanishing of unramified cohomology groups, including the Brauer group, but these consequences do not currently settle rationality in higher dimensions. The unresolved question is whether A1-connectedness is sufficiently strong to force rationality for smooth proper varieties beyond the surface case.