I am looking for an introductive reference to the theory of derived categories. Especially I need to start from the very beginning and I need to know how to use this in examples which comes from algebraic geometry. I don't want a too rigorous approach, made of a lot of definition and propositions but instead I would like to find an introduction which gives the main ideas and many examples. Thank you
Derived category and so on
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reference-request
algebraic-geometry
homological-algebra
arithmetic-geometry
derived-functors
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5Could you expand a bit on your background? How much homological algebra do you know already? I think feeling comfortable with what's in one of Hartshorne's chapters is the bare minimum for such an undertaking to be realistic without too much pain. If you've mastered that, then reading Chapters 1, 2 and 10 of Weibel might be a quite easy place to start (beware the many typos!). Then there's the book of Freitag-Kiehl, (Étale cohomology and the Weil conjectures) containing an exposition specifically adapted to the needs of arithmetic geometry. – 2011-05-16