Lemma 10.134.16. Let $R \to S$ be a ring map of finite type. Let $g \in S$. For any presentations $\alpha : R[x_1, \ldots , x_ n] \to S$, and $\beta : R[y_1, \ldots , y_ m] \to S_ g$ we have

as $S_ g$-modules where $I = \mathop{\mathrm{Ker}}(\alpha )$ and $J = \mathop{\mathrm{Ker}}(\beta )$.

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