On the derived dimension of abelian categories

Abstract

We give an upper bound on the dimension of the bounded derived category of an abelian category. We show that if $\mathcal{X}$ is a sufficiently nice subcategory of an abelian category, then the derived dimension of $\mathcal{A}$ is at most $\mathcal{X}$-dim$\mathcal{A}$, provided that $\mathcal{X}$-dim$\mathcal{A}$ is greater than one. We provide some applications.