Which invariants of a scheme $X$ can be read off from $D^b_c(X, \bar{\mathbf{Q}}_\ell)$ (the bounded derived category of $\bar{\mathbf{Q}}_\ell$-sheaves on $X$, see e.g. [Kiehl-Weissauer])?

What are the precise bounds of your question? Are you asking what invariants can be read off of the triangulated category alone? Or are there certain distinguished objects, like the constant sheaf?
– MoosbruggerOct 20 '11 at 17:39

Yes, of the triangulated category alone.
– Timo KellerNov 13 '11 at 19:22