Bounded t-structures on the category of perfect complexes

TL;DR

This paper proves a conjecture relating the existence of bounded t-structures on the derived category of perfect complexes to the regularity of the scheme, advancing the understanding of triangulated categories.

Contribution

The authors generalize a conjecture by Antieau, Gepner, and Heller, providing new techniques in the theory of approximable triangulated categories to establish the result.

Findings

Bounded t-structures exist if and only if the scheme is regular.

Enhanced techniques for approximable triangulated categories.

Strengthened connection between scheme regularity and derived category structures.

Abstract

Let $X$ be a finite-dimensional, noetherian scheme. Antieau, Gepner and Heller conjectured that its derived category of perfect complexes has a bounded t-structure if and only if $X$ is regular. We prove a generalization, and to do so we sharpen some of the techniques so far obtained in the theory of approximable triangulated categories.