On the derived category of sheaves on a manifold

Abstract

Let $M$ be a non-compact, connected manifold of dimension $\ge 1$. Let $D(\text{sheaves}/M)$ be the unbounded derived category of chain complexes of sheaves of abelian groups on $M$. We prove that $D(\text{sheaves}/M)$ is not a compactly generated triangulated category, but is well generated.