Marco Manetti: Deformations of algebraic schemes via Reedy cofibrant resolutions

Abstract:
In 1976 V. Palamodov (Deformations of complex spaces) introduced the tangent complex L of a complex space X as the differential graded Lie algebra of derivations of a resolvent, and proved that the first and second cohomology group of L give a tangent-obstruction pair for the deformation theory of X. The analogous construction can be easily done in the algebraic setting, for every separated scheme over a field of characteristic 0.

In a joint work with Francesco Meazzini we prove that, up to a slight and harmless additional condition in the definition of the resolvent, the tangent complex controls the deformations of a separated scheme via the general principle of Maurer-Cartan equation modulo gauge equivalence.