%0 Journal Article %T Grothendieck categories and support conditions %A Pierre-Yves Gaillard %J Mathematics %D 2003 %I arXiv %X We give examples of pairs (G1,G2) where G1 is a Grothendieck category and G2 a full Grothendieck subcategory of G1, the inclusion G2 --> G1 being denoted i, for which R^+i : D^+G2 --> D^+G1 (or even Ri : DG2 --> DG1) is a full embedding. This yields generalizations of some results of Bernstein and Lunts, and of Cline, Parshall and Scott. %U http://arxiv.org/abs/math/0309296v4