Construction of Z_p-extensions with prescribed Iwasawa modules

Abstract

We construct Z_p-extensions whose Iwasawa modules have prescribed structure. Specifically, we give a Z_p-extension with prescribed finite Iwasawa module. Also we show that there exists a Z_p-extension with arbitrarily given Iwasawa μ-invariant. We apply the construction of such Z_p-extensions to a certain capitulation problem.