Definition 75.20.2. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $X$, $Y$ be algebraic spaces over $B$. We say $X$ and $Y$ are *Tor independent over $B$* if and only if for every commutative diagram

of geometric points the rings $\mathcal{O}_{X, \overline{x}}$ and $\mathcal{O}_{Y, \overline{y}}$ are Tor independent over $\mathcal{O}_{B, \overline{b}}$ (see More on Algebra, Definition 15.61.1).

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