Marco Manetti: Deformations of algebraic schemes via Reedy cofibrant resolutions
Tid: To 2018-11-01 kl 15.00 - 16.00
Föreläsare: Marco Manetti (Sapienza Università di Roma)
Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University
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.