The Stacks project

Remark 15.91.11. Let $A$ be a ring and let $I \subset A$ be a finitely generated ideal. The left adjoint to the inclusion functor $D_{comp}(A, I) \to D(A)$ which exists by Lemma 15.91.10 is called the derived completion. To indicate this we will say “let $K^\wedge $ be the derived completion of $K$”. Please keep in mind that the unit of the adjunction is a functorial map $K \to K^\wedge $.