On T-Semisimplicity of Iwasawa Modules and Some Computations with Z3-Extensions

Abstract

For certain Zp-extensions of abelian number fields, we study the Iwasawa module associated to the ideal class groups. We show that generic Zp-extensions of abelian number fields are T-semisimple. We also construct the first few layers of the anti-cyclotomic Z3-extension of certain imaginary quadratic number fields and use these to study the Iwasawa modules corresponding to certain Z3-extensions of quadratic and biquadratic fields. In particular, we are able to show in some cases that the Iwasawa module is either finite or T-semisimple.