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ISSN 1088-6826(e) ISSN 0002-9939(p)

On unramified Galois -groups over $\mathbb{Z}_2$ -extensions of real quadratic fields

Author(s): Yasushi Mizusawa
Journal: Proc. Amer. Math. Soc. 138 (2010), 3095-3103.
MSC (2010): Primary 11R23; Secondary 11R20
Posted: May 4, 2010
MathSciNet review: 2653934
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Abstract: We prove that the Galois groups of the maximal unramified pro--extensions over the cyclotomic $\mathbb{Z}_2$ -extensions of certain real quadratic fields are metacyclic pro- groups, and we give some criteria for the finiteness and examples relating to Greenberg's conjecture.

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