## Deformation Theory

### Prof. Barbara Fantechi

This is a course about infinitesimal deformation theory in algebraic geometry. Topics:

- Pseudocategory of Artin rings and Schlessinger functors. Infinitesimal study of schemes: étaleness, unramifiedness, smoothness.
- Elementary deformation theory: definition of smooth schemes, maps, vector bundles.
- The l.c.i. case.
- The general case: the cotangent complex.

References:

- The books of Artin, Sernesi, Hartshorne (on the web), Vistoli (on the ArXiv)