Bousfield localization on formal schemes

AbstractLet (X,OX) be a noetherian formal scheme and consider Dqct(X) its derived category of sheaves with quasi-coherent torsion homology. We show that there is a bijection between the set of rigid (i.e., ⊗-ideals) localizing subcategories of Dqct(X) and subsets in X, generalizing previous work by Neeman. If, moreover, X is separated, the associated localization and acyclization functors are described in certain cases. When Z⊂X is a stable for specialization subset, its associated acyclization is RΓZ. When X is a scheme, the corresponding localizing subcategories are generated by perfect complexes and we recover Thomason's classification of thick subcategories. On the other hand, if Y⊂X is generically stable, we show that the associated localization functor is Hom·X(RΓX⧹YO′X,G)