Construction of Zp-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 $\mu$-invariant. We apply the construction of such $Z_p$-extensions to a certain capitulation problem.