Definition 36.22.2. Let $S$ be a scheme. Let $X$, $Y$ be schemes over $S$. We say $X$ and $Y$ are Tor independent over $S$ if for every $x \in X$ and $y \in Y$ mapping to the same point $s \in S$ the rings $\mathcal{O}_{X, x}$ and $\mathcal{O}_{Y, y}$ are Tor independent over $\mathcal{O}_{S, s}$ (see More on Algebra, Definition 15.61.1).
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