Lemma 33.16.6. Let $f : X \to Y$ be a morphism of schemes over a base scheme $S$. Let $x \in X$ be a point. Set $y = f(x)$. If $\kappa (y) = \kappa (x)$, then $f$ induces a natural linear map

which is dual to the linear map $\Omega _{Y/S, y} \otimes \kappa (y) \to \Omega _{X/S, x}$ via the identifications of Lemma 33.16.4.

## Comments (3)

Comment #3268 by Dario Weißmann on

Comment #3271 by Dario Weißmann on

Comment #3363 by Johan on