On the failure of pseudo-nullity of Iwasawa modules

Yoshitaka Hachimori, Romyar T. Sharifi

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 Zp-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 languageEnglish (US)
Pages (from-to)567-591
Number of pages25
JournalJournal of Algebraic Geometry
Issue number3
StatePublished - Jul 2005

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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