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Lemma 37.13.12. Consider a cartesian diagram of schemes

\[ \xymatrix{ X' \ar[r]_{g'} \ar[d] & X \ar[d] \\ Y' \ar[r] & Y } \]

The canonical map $(g')^*\mathop{N\! L}\nolimits _{X/Y} \to \mathop{N\! L}\nolimits _{X'/Y'}$ induces an isomorphism on $H^0$ and a surjection on $H^{-1}$.

Proof. Translated into algebra this is More on Algebra, Lemma 15.78.2. To do the translation use Lemma 37.13.2. $\square$


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