Lemma 17.21.2. In the situation described above. Let $x \in X$. There are canonical isomorphisms of $\mathcal{O}_{X, x}$-modules $\text{T}(\mathcal{F})_ x = \text{T}(\mathcal{F}_ x)$, $\text{Sym}(\mathcal{F})_ x = \text{Sym}(\mathcal{F}_ x)$, and $\wedge (\mathcal{F})_ x = \wedge (\mathcal{F}_ x)$.

Proof. Clear from Lemma 17.21.1 above, and Algebra, Lemma 10.13.4. $\square$

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