New developments in number theory from the Kummer theory of algebraic tori

在这个研究项目中，我们主要关注代数环面上的有理点群与基域上的极大初等阿贝尔扩展的伽罗瓦群之间的对偶性。这是对经典Kummer理论的自然概括。在基域为素域的情况下，我们还计算了小阶循环群的一般多项式。还研究了几种应用。

In this research project, we are primarily concerned with a duality between the groups of rational points of algebraic tori and the Galois groups of maximal elementary abelian extensions over base fields without roots of unity. This is a natural generalization of the classical Kummer theory. We also compute generic polynomials for cyclic groups of small order in the case where the base field is a prime field. Several applications are also studied.