Proceedings of the Japan Academy, Series A, Mathematical Sciences

Greenberg's conjecture and Leopoldt's conjecture

Norikazu Kubotera

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Abstract

Let $p$ be an odd prime number. We show that the Iwasawa invariants of a certain non-abelian $p$-extension fields of $\mathbf{Q}$ vanish. And we construct non-abelian $p$-extensions over some imaginary quadratic fields satisfying Leopoldt's conjecture on the $p$-adic regulator.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 7 (2000), 108-110.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393469

Digital Object Identifier
doi:10.3792/pjaa.76.108

Mathematical Reviews number (MathSciNet)
MR1785635

Zentralblatt MATH identifier
0971.11053

Subjects
Primary: 11R23: Iwasawa theory 11R27: Units and factorization

Keywords
The Iwasawa invariants Leopoldt's conjecture embedding problems

Citation

Kubotera, Norikazu. Greenberg's conjecture and Leopoldt's conjecture. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 7, 108--110. doi:10.3792/pjaa.76.108. https://projecteuclid.org/euclid.pja/1148393469


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