Bousfield localization on formal schemes

Let be a noetherian formal scheme and consider 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 and subsets in , generalizing previous work by Neeman. If, moreover, is separated, the associated localization and acyclization functors are described in certain cases. When is a stable for specialization subset, its associated acyclization is . When X is a scheme, the corresponding localizing subcategories are generated by perfect complexes and we recover Thomasonʹs classification of thick subcategories. On the other hand, if is generically stable, we show that the associated localization functor is .