Geodesic
Semi-prorepresentability of formal moduli problems and equivariant structures
Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 99-120.

Voir la notice de l'article provenant de la source International Press of Boston

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 semiprorepresentable 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.
DOI : 10.4310/HHA.2024.v26.n2.a5
Classification : 13D10, 14B10, 14D15, 14F35
Keywords: deformation theory, moduli theory, formal moduli problem, equivariance structure 
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     title = {Semi-prorepresentability of formal moduli problems and equivariant structures},
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An-Khuong Doan. Semi-prorepresentability of formal moduli problems and equivariant structures. Homology, homotopy, and applications, Tome 26 (2024) no. 2, pp. 99-120. doi : 10.4310/HHA.2024.v26.n2.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2024.v26.n2.a5/

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