The Stacks project

Definition 61.29.1. Let $\Lambda $ be a Noetherian ring and let $I \subset \Lambda $ be an ideal. Let $X$ be a scheme. An object $K$ of $D(X_{pro\text{-}\acute{e}tale}, \Lambda )$ is called constructible if

  1. $K$ is derived complete with respect to $I$,

  2. $K \otimes _\Lambda ^\mathbf {L} \underline{\Lambda /I}$ has constructible cohomology sheaves and locally has finite tor dimension.

We denote $D_{cons}(X, \Lambda )$ the full subcategory of constructible $K$ in $D(X_{pro\text{-}\acute{e}tale}, \Lambda )$.

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View Definition 61.29.1 as pdf