## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Iwasawa invariants on non-cyclotomic ${\mathbf {Z}_{p}}$-extensions of CM fields

Hideki Goto

#### Abstract

Let $p$ be an odd prime which splits completely into distinct primes in a CM field $K$. By considering ray class field of $K$ with respect to prime ideals lying above $p$, one can define a certain special non-cyclotomic $\mathbf{Z}_{p}$-extension over $K$. We will give some examples of such non-cyclotomic $\mathbf{Z}_{p}$-extensions whose Iwasawa $λ$- and $µ$-invariants both vanish, using a variant of a criterion due to Greenberg.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 9 (2006), 152-154.

Dates
First available in Project Euclid: 4 December 2006

https://projecteuclid.org/euclid.pja/1165244963

Digital Object Identifier
doi:10.3792/pjaa.82.152

Mathematical Reviews number (MathSciNet)
MR2293501

Zentralblatt MATH identifier
1163.11073

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11R29: Class numbers, class groups, discriminants

#### Citation

Goto, Hideki. Iwasawa invariants on non-cyclotomic ${\mathbf {Z}_{p}}$-extensions of CM fields. Proc. Japan Acad. Ser. A Math. Sci. 82 (2006), no. 9, 152--154. doi:10.3792/pjaa.82.152. https://projecteuclid.org/euclid.pja/1165244963