The structure of the Iwasawa module associated with a Zpr-extension of a p-adic local field of characteristic 0

AbstractLet K be a finite extension of Qp. Let K∞, r be a Galois extension of K such that Gr: = Gal(K∞,r/K)≅Zpr for some integer r ≥ 1. Let K∞, rab, p be the maximal abelian pro-p extension of K∞, r, Mr = Gal(K∞, rab, p/K∞, r, and Λr = lim Zp[[Gr/pnGr]]. When r = 1, Iwasawa has determined the Λr-module structure of Mr. In this article we determine the rank and depth of the Λr-module Mr for any integer r ≥ 1