Reconstruction of quasi-compact quasi-separated schemes from categories of perfect complexes

TL;DR

This paper demonstrates how to reconstruct the topological space of a quasi-compact, quasi-separated scheme solely from the tensor triangulated structure of its perfect complexes category.

Contribution

It introduces a method to recover the scheme's underlying space using the tensor triangulated structure of perfect complexes, advancing understanding of scheme reconstruction.

Findings

Reconstruction of the topological space from perfect complexes category

Establishment of a correspondence between tensor triangulated structure and scheme topology

Framework applicable to quasi-compact, quasi-separated schemes

Abstract

We show how to recover the underlying topological space of a quasi-compact quasi-separated scheme from the tensor triangulated structure on its category of perfect complexes.