Tangent lifting of deformations in mixed characteristic

This article presents a new approach to the unobstructedness result for deformations of Calabi-Yau varieties by introducing the tangent lifting property for a functor on artinian local algebras. The verification that the deformation functor of a Calabi-Yau variety in characteristic 0 fulfills the tangent lifting property uses, just as the verification of the $T^1$-lifting property, the degeneration of the Hodge to de Rham spectral sequence. Our main use of our methods is however to the mixed characteristic case. In that case to be able to verify the conditions needed one needs an extension of the criterion introducing divided powers.