On the Derived Category of Sheaves on a Manifold

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

2000 Mathematics Subject Classification: 18E30 55P99 55U35

Keywords and Phrases: Triangulated categories, compactly generated, well generated.

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