Behavior of the curve $x^3+y^3=1$ in a cyclotomic $\Gamma$-extension

This article proves that the group of rational points on the curve in the title remains finite when the $3^n$th roots of unity are adjoined. Here the 3-component of the Tate–Shafarevich group remains finite, and exact formulas are given for its order.
Bibliography: 2 titles.