A spectral sequence for the Hochschild cohomology of a coconnective dga

TL;DR

This paper introduces a spectral sequence for computing Hochschild cohomology of coconnective dgas, enabling the identification of spaces with Noetherian Hochschild cohomology and supporting a theory of support varieties.

Contribution

It presents a new spectral sequence for Hochschild cohomology of coconnective dgas and applies it to identify spaces with Noetherian Hochschild cohomology.

Findings

Spectral sequence for Hochschild cohomology of coconnective dgas.

Identification of spaces with Noetherian Hochschild cohomology.

Development of support variety theory for loop space chains.

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.