Cyclotomic extensions of number fields

Let K be a number field, l a prime number, zeta(l) a primitive l-th root of unity and K-z = K(zeta(l)). In this paper, we first give a detailed description of the discriminant, conductor, different and prime ideal decomposition of the extension K-z/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 K-z modulo lth powers.