The Stacks project

113.7 Deformation theory à la Schlessinger

We have a chapter on this material, see Formal Deformation Theory, Section 90.1. We have a chapter discussing examples of the general theory, see Deformation Problems, Section 93.1. We have a chapter, see Deformation Theory, Section 91.1 which discusses deformations of rings (and modules), deformations of ringed spaces (and sheaves of modules), deformations of ringed topoi (and sheaves of modules). In this chapter we use the naive cotangent complex to describe obstructions, first order deformations, and infinitesimal automorphisms. This material has found some applications to algebraicity of moduli stacks in later chapters. There is also a chapter discussing the full cotangent complex, see Cotangent, Section 92.1.