Definition 37.75.2. Let f : X \to Y be a locally quasi-finite morphism. A weighting or a pondération of f is a map w : X \to \mathbf{Z} such that for any diagram
\xymatrix{ X \ar[d]_ f & U \ar[l]^ h \ar[d]^\pi \\ Y & V \ar[l]_ g }
where V \to Y is étale, U \subset X_ V is open, and U \to V finite, the function \int _\pi (w \circ h) is locally constant.
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