Lemma 15.96.3. Let A \to B be a ring map. Let f \in A be a nonzerodivisor. Let M^\bullet be a bounded complex of finite free A-modules. Assume f maps to a nonzerodivisor g in B. Then I_ i(M^\bullet , f)B = I_ i(M^\bullet \otimes _ A B, g).
Proof. The minors of (f, d^ i) : M^ i \to M^ i \oplus M^{i + 1} map to the corresponding minors of (g, d^ i) : M^ i \otimes _ A B \to M^ i \otimes _ A B \oplus M^{i + 1} \otimes _ A B. \square
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