Wrong Way Recollement for Schemes

Here X is a topological space equal to the union of the closed subset Z and the open complement U , and D(Z), D(X), and D(U) are suitable derived categories of sheaves. The triangulated functors in a recollement must satisfy various conditions, most importantly that (i, i∗), (i∗, i ), (j!, j ), and (j, j∗) are adjoint pairs. The purpose of this note is to point out that, somewhat surprisingly, in the case of schemes, there is also a recollement which goes the other way. By way of notation, if X is a scheme then D(OX), the derived category of sheaves of OX -modules, has the full subcategory D(X) consisting of complexes with quasi-coherent cohomology. If Z is a closed subscheme, there is also the full subcategory DZ(X) consisting of complexes with quasi-coherent cohomology supported on Z.