Definition 51.13.1. Let $I$ be an ideal of a Noetherian ring $A$. Let $K \in D^+_{\textit{Coh}}(A)$. We define the $I$-depth of $K$, denoted $\text{depth}_ I(K)$, to be the maximal $m \in \mathbf{Z} \cup \{ \infty \}$ such that $H^ i_ I(K) = 0$ for all $i < m$. If $A$ is local with maximal ideal $\mathfrak m$ then we call $\text{depth}_\mathfrak m(K)$ simply the depth of $K$.

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