5.7 (1976)

An algebraic variety $X$ over a field $k$ is called rational if the field of functions $k(X)$ is purely transcendental over $k$, and it is called stably rational if $k(X)$ becomes purely transcendental after adjoining finitely many independent variables. Let $T$ be a stably rational torus over a field $k$. Is $T$ rational? Other formulations of this question and some related results see in (V. E. Voskresenskiĭ, Russ. Math. Surveys, 28, no. 4 (1973), 79–105).