Lemma 92.10.3. Let p be a prime number. Let A \to B be a ring homomorphism and assume that p = 0 in A. If A and B are perfect, then L_{B/A} is zero in D(B).
Proof. The map (F_ A, F_ B) : (A \to B) \to (A \to B) is an isomorphism hence induces an isomorphism on L_{B/A} and on the other hand induces zero on L_{B/A} by Lemma 92.10.2. \square
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