Deformation theory for a morphism in the derived category with fixed lift of the codomain

Abstract

We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that semiorthogonal decompositions deform uniquely in smooth proper families of schemes.

15 pages, comments welcome, split off from 2002.03303v2