Lemma 29.35.5. The base change of a morphism which is unramified is unramified. The same holds for G-unramified morphisms.
Proof. The proof of Lemma 29.35.3 shows that being unramified (resp. G-unramified) is a local property of ring maps. Hence the lemma follows from Lemma 29.14.6 combined with the fact that being unramified (resp. G-unramified) is a property of ring maps that is stable under base change, see Algebra, Lemma 10.151.3. $\square$
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