Iwasawa's constant $μ$ vanishes in cyclotomic $\Z_p$-extensions of CM fields

Details Iwasawa's constant $μ$ vanishes in cyclotomic $\Z_p$-extensions of CM fields Iwasawa's constant $μ$ vanishes in cyclotomic $\Z_p$-extensions of CM fields

2011-05-10

arxiv.org/abs/1105.1970v2

Mathematics

Number Theory

The proof of Lemma 7 contains a gap that I currently cannot fill. Therefore the proof is presently on ice - the approach possi

Scientific paper

Let $\K$ be a galois CM extension of $\Q$ and $\K_{\infty}$ its cyclotomic
$\Z_p$-extension. Let $A_n$ be the $p$-parts of the class groups in the
intermediate subfields $\K_n \subset \K_{\infty}$ and $\rg{A} = \varprojlim_n
A_n$. We show that the $p$-rank of $\rg{A}$ is finite, which is equivalent to
the vanishing of Iwasawa's constant $\mu$ for $\rg{A}$. (Currently withdrawn)

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