OBSTRUCTION CALCULUS FOR FUNCTORS OF ARTIN RINGS, I

In this paper we define and study obstruction theories for morphisms o f functors of Artin rings. We prove the existence of a universal obstr uction theory, and we give explicit criteria for completeness and for linearity. As applications, we extend several results in the literatur e, removing the finite-dimensionality of the tangent space and the exi stence of a vector space of obstructions from the assumptions. (C) 199 8 Academic Press.