TY - JOUR
T1 - On the failure of pseudo-nullity of Iwasawa modules
AU - Hachimori, Yoshitaka
AU - Sharifi, Romyar T.
PY - 2005/7
Y1 - 2005/7
N2 - 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.
AB - 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.
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U2 - 10.1090/S1056-3911-05-00396-6
DO - 10.1090/S1056-3911-05-00396-6
M3 - Article
AN - SCOPUS:20444452542
SN - 1056-3911
VL - 14
SP - 567
EP - 591
JO - Journal of Algebraic Geometry
JF - Journal of Algebraic Geometry
IS - 3
ER -