Lemma 29.32.18. Let

be a commutative diagram of schemes where $i$ and $j$ are immersions. Then there is a canonical exact sequence

where the first arrow comes from Lemma 29.31.3 and the second from Lemma 29.32.15.

Lemma 29.32.18. Let

\[ \xymatrix{ Z \ar[r]_ i \ar[rd]_ j & X \ar[d] \\ & Y } \]

be a commutative diagram of schemes where $i$ and $j$ are immersions. Then there is a canonical exact sequence

\[ \mathcal{C}_{Z/Y} \to \mathcal{C}_{Z/X} \to i^*\Omega _{X/Y} \to 0 \]

where the first arrow comes from Lemma 29.31.3 and the second from Lemma 29.32.15.

**Proof.**
The algebraic version of this is Algebra, Lemma 10.134.7.
$\square$

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