The Stacks project

Lemma 36.3.7. If $f : X \to Y$ is a morphism of affine schemes given by the ring map $A \to B$, then the diagram

\[ \xymatrix{ D(B) \ar[d] \ar[r] & D_\mathit{QCoh}(\mathcal{O}_ X) \ar[d]^{Rf_*} \\ D(A) \ar[r] & D_\mathit{QCoh}(\mathcal{O}_ Y) } \]

commutes.

Proof. Follows from Lemma 36.3.5 using that $R\Gamma (Y, Rf_*K) = R\Gamma (X, K)$ by Cohomology, Lemma 20.32.5. $\square$

Comments (2)

Comment #4289 by David Hansen on

In the commutative square here, A and B should be swapped.

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