Generating the bounded derived category and perfect ghosts

TL;DR

This paper proves that for many abelian categories, the bounded derived category contains no non-trivial strongly finitely generated thick subcategories that include all perfect complexes, using a new version of the Ghost Lemma.

Contribution

It introduces a strong converse of the Ghost Lemma for bounded derived categories, advancing understanding of their subcategory structure.

Findings

Bounded derived categories lack non-trivial strongly finitely generated thick subcategories containing all perfect complexes.

A new strong converse of the Ghost Lemma is established for these categories.

Results apply to categories relevant in representation theory and algebraic geometry.

Abstract

We show, for a wide class of abelian categories relevant in representation theory and algebraic geometry, that the bounded derived categories have no non-trivial strongly finitely generated thick subcategories containing all perfect complexes. In order to do so we prove a strong converse of the Ghost Lemma for bounded derived categories.