Basic Deformation Theory of Smooth Formal Schemes
نویسنده
چکیده
We provide the main results of a deformation theory of smooth formal schemes as defined in [2]. Smoothness is defined by the local existence of infinitesimal liftings. Our first result is the existence of an obstruction in a certain Ext group whose vanishing guarantees the existence of global liftings of morphisms. Next, given a smooth morphism f0 : X0 → Y0 of noetherian formal schemes and a closed immersion Y0 →֒ Y given by a square zero ideal I, we prove that the set of isomorphism classes of smooth formal schemes lifting X0 over Y is classified by Ext(b Ω1X0/Y0 , f ∗ 0 I) and that there exists an element in Ext(b Ω1X0/Y0 , f ∗ 0 I) which vanishes if and only if there exists a smooth formal scheme lifting X0 over Y.
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