We construct -extensions whose Iwasawa modules have prescribed structure. Specifically, we give a -extension with prescribed finite Iwasawa module. Also we show that there exists a -extension with arbitrarily given Iwasawa -invariant. We apply the construction of such -extensions to a certain capitulation problem.
Manabu OZAKI. "Construction of -extensions with prescribed Iwasawa modules." J. Math. Soc. Japan 56 (3) 787 - 801, July, 2004. https://doi.org/10.2969/jmsj/1191334086