  A spectral sequence for the computation of the Hochschild cohomology of a
coconnective dga over a field is presented. This spectral sequence has a
similar flavour to the spectral sequence constructed by Cohen, Jones and Yan
for the computation of the loop homology of a closed orientable manifold. Using
this spectral sequence we identify a class of spaces for which the Hochschild
cohomology of their mod-p cochain algebra is Noetherian. This implies, among
other things, that for such a space the derived category of mod-p chains on its
loop-space carries a theory of support varieties.
