Abstract
Let k be a real quadratic number field, and k∞ its cyclotomic Z2-extension. We study the cyclicity of the Galois group X∞′ over k∞ of the maximal abelian unramified 2-extension, in which all 2-adic primes of k∞ split completely. As consequence, we determine the complete list of real quadratic number fields for which X∞′ is cyclic.When X∞′ is cyclic non-trivial, we give a new infinite family of real quadratic number fields, for which Greenberg's conjecture is valid.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
