The relation type of analytic and formal algebras

Abstract

We introduce the notion of relation types for analytic and formal k-algebras, extending a result by F. Planas-Vilanova to affine k-algebras. We establish the well-definedness and invariance of this notion by characterizing it in terms of André-Quillen homology and utilizing the Jacobi-Zariski long exact sequence of homology. In particular, we show that the relation type is an invariant of schemes of finite type over a field, analytic varieties, and algebroid varieties. We also provide a discussion and analysis of relation types for certain special varieties.