Cyclotomic extensions of number fields

AbstractLet K be a number field, l a prime number, ζl a primitive l-th root of unity and Kz = K(ζl). In this paper, we first give a detailed description of the discriminant, conductor, different and prime ideal decomposition of the extension Kz/K. We apply this to obtain the Galois-module structure of certain finite modules associated to prime ideals above l, and we also give the Galois-module structure of the unit group of Kz modulo lth powers