Basic deformation theory of smooth formal schemes

الأصل · EN

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 Ext¹ 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 Ext¹ group and there exists an obstruction in a Ext² group whose vanishing characterizes the existence of smooth liftings.