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Jun 17, 2013 at 15:31 comment added Martin Brandenburg Unfortunately there is not the derived category $D(X)$ of a scheme or stack $X$, although this notation is used quite often. But it can refer to the bounded, bounded below, bounded above derived category of the abelian category of Zariski, étale, lisse-étale etc. quasi-coherent or coherent sheaves on $X$ ...
May 10, 2013 at 18:16 comment added Fernando Muro @Simon, I apologize in advance if my suggestion is innapropriate, but if you're not familiar with derived categories I would first go for derived categories of rings, then for derived categories of Grothendieck abelian categories, and finally I'd consider the particular cases you're interested in.
May 10, 2013 at 17:52 answer added user1437 timeline score: 4
May 10, 2013 at 16:45 comment added Dylan Wilson The Stacks Project is great!
May 10, 2013 at 16:44 comment added Damian Rössler There is the first chapter of the book "Sheaves on manifolds" by Kashiwara-Shapira.
May 10, 2013 at 15:07 answer added Libli timeline score: 2
May 10, 2013 at 15:04 history asked Simon Rose CC BY-SA 3.0