MOS

Abstract

This series of three lectures aims to give an introduction to the algebraic approach to deformation theory, as developed by Grothendieck, Schlessinger, Illusie and Artin, illustrated with a few key examples.

The topics will include (i) infinitesimal theory over Artin local rings including Schlessinger's theorem, tangent-obstruction theories and use of cotangent complex, (ii) algebraization via the Grothendieck existence theorem for formal schemes and the Artin approximation theorem, and (iii) construction of global moduli as quotient algebraic spaces.