bserve that $\mathcal{S}_0^{{\ifm {{\sf wt}} {{$\sf wt$}}}_0}$ is a nonzero polynomial of ${\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_s {\ifm {,\ldots,} {$,\ldots,$}}A_0)[A_0,A_0]$, and $${\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_s {\ifm {,\ldots,} {$,\ldots,$}}A_0)[A_0,A_0]/(\mathcal{S}_0^{{\ifm {{\sf wt}} {{$\sf wt$}}}_0}) \simeq {\overline{{\mathbb F}}_{\hskip-0.0mm q}}(A_s {\ifm {,\ldots,} {$,\ldots,$}}A_0)[A_0