The Stacks project

Definition 115.23.7. Let $(S, \delta )$ be as in Chow Homology, Situation 42.7.1. Let $X$ be locally of finite type over $S$. Assume $X$ integral and $\dim _\delta (X) = n$. Let $D_1, D_2$ be two effective Cartier divisors in $X$. Let $Z \subset X$ be an integral closed subscheme with $\dim _\delta (Z) = n - 1$. The $\epsilon $-invariant of this situation is

\[ \epsilon _ Z(D_1, D_2) = n_ Z \cdot m_ Z \]

where $n_ Z$, resp. $m_ Z$ is the coefficient of $Z$ in the $(n - 1)$-cycle $[D_1]_{n - 1}$, resp. $[D_2]_{n - 1}$.

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