Lemma 115.11.5. Let $f : X \to Y$ be a morphism schemes. Assume

$X$ and $Y$ are integral schemes,

$f$ is locally of finite type and dominant,

$f$ is either quasi-compact or separated,

$f$ is generically finite, i.e., one of (1) – (5) of Morphisms, Lemma 29.51.7 holds.

Then there is a nonempty open $V \subset Y$ such that $f^{-1}(V) \to V$ is finite locally free of degree $\deg (X/Y)$. In particular, the degrees of the fibres of $f^{-1}(V) \to V$ are bounded by $\deg (X/Y)$.

## Comments (3)

Comment #5549 by Hao on

Comment #5551 by Laurent Moret-Bailly on

Comment #5734 by Johan on