Iwasawa's μ=0 conjecture for cyclotomic ℤp-extensions

Let $K$ be a number field and let $K^{\text{cyc}}$ be the cyclotomic $\mathbf{Z}_p$-extension of $K$. The Iwasawa $\mu$-invariant is the coefficient governing the exponential term in the asymptotic growth of the $p$-part of class numbers in the tower. Iwasawa's μ=0 conjecture. The invariant satisfies $\mu=0$. This is a central open problem in classical Iwasawa theory; it is known when $K/\mathbf{Q}$ is abelian by Ferrero and Washington, but remains open in general.