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

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

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

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

## Comments (0)