Strong Generators in Dperf(X) for Schemes with a Separator

TL;DR

This paper generalizes Neeman's criteria for strong generators in the derived category of perfect complexes to a broader class of schemes with separators, enhancing understanding of their categorical properties.

Contribution

It extends Neeman's results from separated schemes to schemes with separators, providing new conditions for the regularity of Dperf(X) and implications for functor representability.

Findings

Extended strong generator criteria to schemes with separators

Characterized regularity conditions for Dperf(X)

Linked properness over noetherian rings to functor representability

Abstract

This paper extends the result from Amnon Neeman regarding strong generators in Dperf(X), from X being a quasicompact, separated scheme to X being quasicompact, quasiseparated scheme that admits a separator. Neeman's result states a necessary and sufficient condition for Dperf(X) being regular. Together with being proper over a noetherian commutative ring, those conditions give an interesting description for when an R-linear functor H is representable.