  Let (X, O_X) be a noetherian formal scheme and consider D_qct(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. \tensor-ideals) localizing
subcategories of D_qct(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 \Gamma_Z. 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.
