A spectral sequence for the Hochschild cohomology of a coconnective dga

Abstract

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.Comment: Final version. The new version adds an application of the results to the construction of support varieties for modules over the chains algebra of certain loop-spaces. See Corollary 1.7 and Proposition 2.