As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks?

My primary concern is that since these languages are more or less standard in many (if not all) aspects of algebraic geometry, why not introduce them as early as possible? Someone might argue these are not motivated very well at early stages of learning. But considering the amount of commutative algebra and classical homological algebra being used by (or at least developed within) a rigorous abstract algebraic geometry textbook (e.g. Hartshorne's, Qing Liu's, etc.), it is no fault to introduce the modern common language in the first place once and for all and leave to the beginners for years' digestion.

introductionto algebraic geometry is badly mistaken. It is like advocating that introductory physics should include General Relativity and quantum mechanics, since those are more or less standard in many aspects of physics at the professional level. The challenges of education are serious. $\endgroup$ – user74230 Dec 15 '14 at 22:117more comments