Quasiexcellence implies strong generation

TL;DR

This paper proves that the bounded derived category of coherent sheaves on certain schemes has a strong generator, extending recent results and using advanced algebraic geometry tools.

Contribution

It establishes the existence of strong generators for derived categories on quasicompact separated quasiexcellent schemes, generalizing previous work and including the affine case.

Findings

Strong generators exist for derived categories on quasicompact separated quasiexcellent schemes.

The result applies even in the affine case, broadening previous scope.

Uses Gabber's weak local uniformization theorem and morphism properties.

Abstract

We prove that the bounded derived category of coherent sheaves on a quasicompact separated quasiexcellent scheme of finite dimension has a strong generator in the sense of Bondal-Van den Bergh. This extends a recent result of Neeman and is new even in the affine case. The main ingredient includes Gabber's weak local uniformization theorem and the notions of boundedness and descendability of a morphism of schemes.