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Jan 5, 2015 at 21:51 vote accept Qiao
Jul 20, 2010 at 22:20 comment added Ryan Reich That's true. It's not clear which parts are necessary, but I think in fact that just about everything is relevant since so much of the theory of schemes has word-for-word generalizations to stacks. However, simply to understand the definition of an algebraic stack, you need at least to really appreciate the concept of base change (i.e. fibered product) and know what a smooth morphism is. To understand what is going on, you also have to love the functor of points. This is experiential knowledge; you can't research it, you can only assimilate it. Hence, "learn algebraic geometry first".
Jul 20, 2010 at 22:06 comment added Charles Staats Telling someone "you should learn algebraic geometry" is like telling them "you should learn math." Obviously you don't mean all of it, but it's not clear which parts are necessary/relevant, or where the stopping point should be.
Jul 20, 2010 at 19:03 history edited Ryan Reich CC BY-SA 2.5
Modulate tone
Jul 20, 2010 at 16:23 history answered Ryan Reich CC BY-SA 2.5