2021/07/20 by Doan, An Khuong
#13D10 #14B10 #14D15 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.09505
We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an analogue of Schlessinger's conditions for a functor of Artinian rings to have a semi-universal element. We also give a sufficient condition for a semi-prorepresentable formal moduli problem to admit a G-equivariant structure in a sense specified below, where G is a linearly reductive group. Finally, by making use of these criteria, we derive many classical results including the existence of (G-equivariant) formal semi-universal deformations of algebraic schemes and that of complex compact manifolds.