GAGA type results for singularity categories

Several GAGA-type results for singularity categories are presented. Firstly, as an easy consequence of Serre's GAGA theorem, we show that for a complex projective variety, its singularity category is naturally equivalent to that of its analytification. Secondly, we introduce the torsion singularity category of a formal scheme. Under Orlov's (ELF) condition, we prove that for the formal completion of a Noetherian scheme along a closed subset, its torsion singularity category is equivalent to the singularity category of the original scheme, with support in the closed subset. Lastly, using the Artin Approximation Theorem and the result above, we provide an alternative proof of a result of Orlov. Namely, for a Noetherian local ring with an isolated singularity, its singularity category is equivalent (up to direct summands) to that of its Henselization, which in turn is equivalent to that of its completion.