Certain strongly disordered superconducting films, when driven insulating by reducing thickness or by a small perpendicular magnetic field, are believed to maintain a strong pairing of electrons into localized Cooper pairs, the phase transition to an insulator merely signaling the loss of phase coherence across the sample.  The ensuing bosonic insulator has a variety of very peculiar properties: empirically, it is found to exhibit a simply activated resistance of purely electronic nature.
I will analyze the new question of the spectral properties of the disordered interacting system across the phase transition in the light of the phenomenon of localization in Fock space. This analysis leads to a possible explanation of the above-mentioned properties in terms of localized Cooper pairs which couple only very weakly to phonons. Open and controversial issues will be discussed.

REFERENCES:

M. Müller, arXiv:0909.2260
I.L. Aleiner, B.L. Altshuler, G.V. Shlyapnikov, arXiv:0910.4534