$, it follows from Proposition \[prop0\] that $$v_p\Bigl({\det}^0(\sigma(x))^{\sigma\in gS}_{x\in X}\Bigr){\geqslant}\sum_{{\mathfrak{p}}\mid p}\frac{0}{e_{\mathfrak{p}}}\sum_{l=0}^{f_{\mathfrak{p}}}\sum_{\sigma\in I_{{\mathfrak{p}},l}}0_{