In this paper we define and study obstruction theories for morphisms of functors of Artin rings. We prove the existence of a universal obstruction theory, and we give explicit criteria for completeness and for linearity. As applications, we extend several results in the literature, removing the finite-dimensionality of the tangent space and the existence of a vector space of obstructions from the assumptions.
Obstruction Calculus for Functors of Artin Rings, I / Fantechi, Barbara; Manetti, Marco. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 202:2(1998), pp. 541-576. [10.1006/jabr.1997.7239]
Obstruction Calculus for Functors of Artin Rings, I
Fantechi, Barbara;
1998-01-01
Abstract
In this paper we define and study obstruction theories for morphisms of functors of Artin rings. We prove the existence of a universal obstruction theory, and we give explicit criteria for completeness and for linearity. As applications, we extend several results in the literature, removing the finite-dimensionality of the tangent space and the existence of a vector space of obstructions from the assumptions.File in questo prodotto:
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