Lemma 50.23.10. Let c \geq 0 and
\xymatrix{ Z' \ar[d]_ h \ar[r] & X' \ar[d]_ g \ar[r] & S' \ar[d] \\ Z \ar[r] & X \ar[r] & S }
satisfy the assumptions of Lemma 50.23.6 and assume in addition that X \to S and X' \to S' are smooth and that Z \to X and Z' \to X' are Koszul regular immersions. Then the diagram
\xymatrix{ H^ q(Z, \Omega ^ p_{Z/S}) \ar[rr]_-{\gamma ^{p, q}} \ar[d] & & H^{q + c}(X, \Omega ^{p + c}_{X/S}) \ar[d] \\ H^ q(Z', \Omega ^ p_{Z'/S'}) \ar[rr]^{\gamma ^{p, q}} & & H^{q + c}(X', \Omega ^{p + c}_{X'/S'}) }
is commutative where \gamma ^{p, q} is as in Remark 50.23.7.
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