Authors: 1) Karin Erdmann Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB 2) Miles Holloway Mathematical Institute, 24-29 St Giles, Oxford OX1 3LB Abstract: We present a new proof of the Avrunin Scott theorem identifying the support variety of an elementary abelian p-group with its rank variety. Our proof uses a representation theoretic perspective. We then use these ideas to prove the analogue of the Avrunin Scott theorem for a certain class of local algebras which has both a support variety (defined in terms of Hochschild cohomology) and a rank variety. Status: Preprint. Submitted to Journal of Algebra.