Comparison theorems for deformation functors via invariant theory
Journal article, Peer reviewed
Accepted version
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https://hdl.handle.net/10642/6596Utgivelsesdato
2018-09-06Metadata
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Originalversjon
Christophersen JA, Kleppe JO. Comparison theorems for deformation functors via invarianttheory. Collectanea Mathematica. 2018 http://dx.doi.org/10.1007/s13348-018-0232-zSammendrag
We compare deformations of algebras to deformations of schemes in the setting of invariant theory. Our results generalize comparison theorems of Schlessinger and the second author for projective schemes. We consider deformations (abstract and embedded) of a scheme X which is a good quotient of a quasi-affine scheme X0 by a linearly reductive group G and compare them to invariant deformations of an affine G-scheme containing X0 as an open invariant subset. The main theorems give conditions for when the comparison morphisms are smooth or isomorphisms.