The Stacks project

Definition 61.29.4. Let $X$ be a scheme. Let $\Lambda $ be a Noetherian ring and let $I \subset \Lambda $ be an ideal. Let $K \in D(X_{pro\text{-}\acute{e}tale}, \Lambda )$.

1. We say $K$ is adic lisse¹ if there exists a finite complex of finite projective $\Lambda ^\wedge $-modules $M^\bullet $ such that $K$ is locally isomorphic to

   \[ \underline{M^ a}^\wedge \to \ldots \to \underline{M^ b}^\wedge \]

2. We say $K$ is adic constructible² if for every affine open $U \subset X$ there exists a decomposition $U = \coprod U_ i$ into constructible locally closed subschemes such that $K|_{U_ i}$ is adic lisse.