We investigate how to compare Hochschild cohomology of algebras related by a
Morita context. Interpreting a Morita context as a ring with distinguished
idempotent, the key ingredient for such a comparison is shown to be the grade
of the Morita defect, the quotient of the ring modulo the ideal generated by
the idempotent. Along the way, we show that the grade of the stable
endomorphism ring as a module over the endomorphism ring controls vanishing of
higher groups of selfextensions, and explain the relation to various forms of
the Generalized Nakayama Conjecture for Noetherian algebras. As applications of
our approach we explore to what extent Hochschild cohomology of an invariant
ring coincides with the invariants of the Hochschild cohomology.Comment: 28 pages, uses conm-p-l.sty. To appear in Contemporary Mathematics
series volume (Conference Proceedings for Summer 2001 Grenoble and Lyon
conferences, edited by: L. Avramov, M. Chardin, M. Morales, and C. Polini
