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

Nagaraj, D. S. (1991) The structure of the Iwasawa module associated with a Zpr-extension of a p-adic local field of characteristic 0 Journal of Number Theory, 38 (1). pp. 52-57. ISSN 0022-314X

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0022-314X(91)90092-P

Abstract

Let 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[[ G r/pn G r]]. 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.

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