The Avrunin and Scott theorem and a truncated polynomial algebra

We prove an analogue of a theorem of Avrunin and Scott for truncated polynomial algebras over an algebraically closed field of arbitrary characteristic. The Avrunin and Scott theorem relates the support variety for a finite-dimensional kE-module to its rank variety (where char(k)=p and E is an elementary abelian p-group). The analogue of the Avrunin and Scott theorem relates the support variety for a finite-dimensional Λm-module (using Hochschild cohomology) to its rank variety (developed in [K. Erdmann, M. Holloway, Rank varieties and projectivity for a class of local algebras, Math. Z. 247 (2004) 441–460] using Clifford algebras). Along the way to proving our main result we provide a new proof of the Avrunin and Scott theorem for elementary abelian p-group algebras which we are then able to generalise to the setting of Λm-algebras.