On the failure of pseudo-nullity of Iwasawa modules

Details On the failure of pseudo-nullity of Iwasawa modules On the failure of pseudo-nullity of Iwasawa modules

2004-06-18

arxiv.org/abs/math/0406366v2

J. Algebraic Geom. 14 (2005), 567-591

Mathematics

Number Theory

26 pages

Scientific paper

We 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 lambda-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 assumption that mu is trivial. This proof uses certain exact sequences involving Iwasawa modules in procyclic extensions. These sequences are derived in an appendix by the second author.

Affiliated with

Also associated with

No associations

Rating

On the failure of pseudo-nullity of Iwasawa modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the failure of pseudo-nullity of Iwasawa modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the failure of pseudo-nullity of Iwasawa modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203778