Definition 47.27.1. Let $R \to A$ be a flat ring map of finite presentation. A *relative dualizing complex* is an object $K \in D(A)$ such that

$K$ is $R$-perfect (More on Algebra, Definition 15.78.1), and

$R\mathop{\mathrm{Hom}}\nolimits _{A \otimes _ R A}(A, K \otimes _ A^\mathbf {L} (A \otimes _ R A))$ is isomorphic to $A$.

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