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December 2006 Iwasawa invariants on non-cyclotomic ${\mathbf {Z}_{p}}$-extensions of CM fields
Hideki Goto
Proc. Japan Acad. Ser. A Math. Sci. 82(9): 152-154 (December 2006). DOI: 10.3792/pjaa.82.152


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.


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Hideki Goto. "Iwasawa invariants on non-cyclotomic ${\mathbf {Z}_{p}}$-extensions of CM fields." Proc. Japan Acad. Ser. A Math. Sci. 82 (9) 152 - 154, December 2006.


Published: December 2006
First available in Project Euclid: 4 December 2006

zbMATH: 1163.11073
MathSciNet: MR2293501
Digital Object Identifier: 10.3792/pjaa.82.152

Primary: 11R23
Secondary: 11R29

Keywords: $\mathbf {Z}_{p}$-extensions , Greenberg conjecture , Iwasawa invariants

Rights: Copyright © 2006 The Japan Academy

Vol.82 • No. 9 • December 2006
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