## Abstract

Consider the family of CM-fields which are pro-p p-adic Lie extensions of number fields of dimension at least two, which contain the cyclotomic Z _{p}-extension, and which are ramified at only finitely many primes. We show that the Galois groups of the maximal unramified abelian pro-p extensions of these fields are not always pseudo-null as Iwasawa modules for the Iwasawa algebras of the given p-adic Lie groups. The proof uses Kida's formula for the growth of λ-invariants in cyclotomic Z_{p}-extensions of CM-fields. In fact, we give a new proof of Kida's formula which includes a slight weakening of the usual μ = 0 assumption. This proof uses certain exact sequences involving Iwasawa modules in pro-cyclic extensions. These sequences are derived in an appendix by the second author.

Original language | English (US) |
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Pages (from-to) | 567-591 |

Number of pages | 25 |

Journal | Journal of Algebraic Geometry |

Volume | 14 |

Issue number | 3 |

DOIs | |

State | Published - Jul 2005 |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology