Ramification groups of nonabelian Kummer extensions (Q1360714)

The author uses work of Coleman, McCallum and that of Prapavessi in which the conductor of the abelian Kummer extensions \(\mathbb{Q}_p (\root p^n\of a,\zeta_{p^n})/\mathbb{Q}_p(\zeta_{p^n})\) \((a\in\mathbb{Q}_p\), \(\zeta_{p^n}\) is a primitive \(p^n\)th root of unity for a fixed prime \(p\) and all positive integers \(n\)) and computes the ramification groups of non-abelian Kummer extension \(\mathbb{Q}_p (\root p^\infty\of {\mathbb{Q}_p^*})/\mathbb{Q}_p\) obtained from adjoining to \(\mathbb{Q}_p\) all \(p\)-power roots of its elements.