Ihara's isomorphism conjecture for the stable derivation algebra

Let $\mathfrak g$ be the graded ${\mathbb Z}_p$-Lie algebra associated with the weight filtration on the pro-$p$ Galois action, let $\mathcal D$ be Ihara's stable derivation algebra, and let

$$\iota\colon\mathfrak g\longrightarrow\mathcal D\otimes{\mathbb Z}_p$$

be Ihara's injection. Ihara's isomorphism conjecture. The induced map

$$\operatorname{gr}^m\iota$$

is an isomorphism for $m<p$. Ihara's injection compares the Galois Lie algebra with the stable derivation algebra; the conjecture asserts that the comparison is exact in all degrees below $p$.