Bousfield localization on formal schemes

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Let (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 is a stable for specialization subset of X, its associated acyclization is ΓZ. When X is an 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 is a generically stable subset of X, we give an expression for the associated localization functor.