Abstract
We shall show two sufficient conditions under which the Iwasawa invariants λ k and μ k of a totally real fieldk vanish for an odd primel, based on the results obtained in [1], [3] and [4]. LetKn be the composite ofk and theln-th cyclotomic extension of the fieldQ of rational numbers. LetCn be the factor group of thel-class group ofKn by a subgroup generated by ideals whose prime factors divide the principal ideal (l). Let ϕ1 be an idempotent of the group ringZl[Gal(K1/k)] defined in the below. We shall prove λ k = μ k =0 if there is a natural numbern such that e1C n vanishes, under additional conditions concerning ramifications inKn/k.
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.
