Algebraicity and algebraizability

We will recall the notion of algebraizability of perfect complexes on a formal neighborhood of a closed subscheme: these are perfect complexes which are generated (via cones, shifts and direct sumands) by the restrictions of perfect complexes on the ambient scheme. We will state several results stating that in some situations algebraizability is equivalent to algebraicity of certain power series. A special case is covered in the recent preprint 1711.00756.