English

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

Algebraic Geometry 2025-11-14 v1 Category Theory

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.

Keywords

Cite

@article{arxiv.2511.10312,
  title  = {Deformation theory for a morphism in the derived category with fixed lift of the codomain},
  author = {Pieter Belmans and Wendy Lowen and Shinnosuke Okawa and Andrea T. Ricolfi},
  journal= {arXiv preprint arXiv:2511.10312},
  year   = {2025}
}

Comments

15 pages, comments welcome, split off from 2002.03303v2