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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 theintermediate subfields $\K_n \subset \K_{\infty}$ and $\rg{A} = \varprojlim_nA_n$. We show that the $p$-rank of $\rg{A}$ is finite, which is equivalent tothe vanishing of Iwasawa's constant $\mu$ for $\rg{A}$. (Currently withdrawn)

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