Boyd's homological formulation of the $K(\pi,1)$ conjecture

Let $A_\Gamma^+$ be the Artin monoid associated with an Artin group $A_\Gamma$, and let $\mathbb Z A_\Gamma^+$ and $\mathbb Z A_\Gamma$ be their monoid and group rings. The inclusion $A_\Gamma^+\hookrightarrow A_\Gamma$ induces the relevant extension of scalars. Boyd's conjecture. One has

$$\operatorname{Tor}_*^{\mathbb Z A_\Gamma^+}(\mathbb Z A_\Gamma,\mathbb Z)=0$$

for all $*\geq 1$. This homological vanishing is presented as equivalent to the $K(\pi,1)$ conjecture, via the homotopy equivalence of the classifying spaces of the Artin monoid and group.