Basic deformation theory of smooth formal schemes

Details Basic deformation theory of smooth formal schemes Basic deformation theory of smooth formal schemes

2008-01-18

arxiv.org/abs/0801.2846v1

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We provide the main results of a deformation theory of smooth formal schemes. First we deal with the case of global lifting of smooth morphisms. We prove that the obstruction to the existence of a global lifting lies in a Ext^1 group. Then we study uniqueness and existence of lifting of smooth formal schemes. The set of isomorphism classes of smooth liftings is classified by a Ext^1 group and there exists an obstruction in a Ext^2 group whose vanishing characterizes the existence of smooth liftings.

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