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
\[ \xymatrix{ \mathop{\mathrm{Spec}}(k) \ar[d]_{\overline{y}} \ar[dr]_{\overline{b}} \ar[r]_-{\overline{x}} & X \ar[d] \\ Y \ar[r] & B } \]
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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