Theorem B.7 (Subadditivity) . [01I7]

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Theorem B.7 (Subadditivity).

Let $\mathcal{X}$ be a regular model, $\mathfrak{a},\mathfrak{b}$ vertical coherent ideal sheaves on $\mathcal{X}$ and $c,d>0$ . Then we have

\mathcal{J}(\mathfrak{a}^{c}\cdot\mathfrak{b}^{d})\subset\mathcal{J}(\mathfrak{a}^{c})\cdot\mathcal{J}(\mathfrak{b}^{d}).