Introduction

Abstract

Deformation theory is the local study of deformations. Or, seen from another point of view, it is the infinitesimal study of a family in the neighborhood of a given element. A typical situation would be a flat morphism of schemes f : X → T. For varying t ∈ T we regard the fibers X_t as a family of schemes. Deformation theory is the infinitesimal study of the family in the neighborhood of a special fiber X₀.