Kummer–Vandiver conjecture on cyclotomic class-group eigenspaces

Let $l$ be a prime, let $A=Cl(\mathbb Z[\mu_l])_l$, and let $A^{[i]}$ be the eigenspace corresponding to the $i$-th power of the Teichmüller character $\omega:G(\mathbb Q(\mu_l)/\mathbb Q)\to(\mathbb Z/l\mathbb Z)^\times$. Kummer–Vandiver conjecture.

$$A^{[l-1-n]}=0$$

for all even $n$ with $0\leq n\leq l-1$. This is one of the classical conjectures in cyclotomic field theory; the source gives no resolution status.