Decomposition and inertia groups in \({\mathbb{Z}}_ p\)-extensions
The author gives a description of the decomposition, inertia, and higher ramification groups in a \({\mathbb{Z}}_ p\)-extension of a number field k. This is accomplished via a logarithm function [the author, J. Reine Angew. Math. 343, 64-80 (1983; Zbl 0501.12015)] which gives a canonical isomorphism between the Galois group of the compositum of all \({\mathbb{Z}}_ p\)-extensions of k and a certain \({\mathbb{Z}}_ p\)-module attached to k. The case of imaginary quadratic fields is worked out in detail.
scientific article; zbMATH DE number 3979186