Can somebody give me a good reference book on stacks? I learned my algebraic geometry mostly with Görtz and Wedhorn's book, and I wonder if there's a book on the theory of stacks that is equally comprehensive?

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    $\begingroup$ I haven't read it, so I'm just posting a comment, but I've heard good things about Martin Olssons's book Algebraic Spaces and Stacks. $\endgroup$ May 1 '20 at 15:37

I really like Olsson's book. This does, if Alex comes back to this question, make me one of the people that he mentioned in his comment.

Actually, I am reading Olsson's book at the moment and I think the ideas are motivated in a nice and understandable way. In particular at the beginning of each chapter. Moreover, I really like how explicit he is even when things are very technical. I did at least so far not have the feeling that he was trying to hide something or that he was too lazy to really give the argument.

There are enough examples (even some example subsections) and they are really placed well within the book. Whenever I really craved for some, I got some.

I also like the way he is reminding you of some things you should have seen before, like etale things. He is redefining them most of the times (if not all the time) without spending too much time on them so that you don't loose focus on what you actually want to do in each chapter.

Furthermore, there are various exercises ranging from rather casual verifications to more serious problems.

There are probably more things I could say, but I guess I made quite clear that I think that this book is well written and thought through.

Otherwise, there are various nice notes that you can find online by Vakil, Fantechi or Vistoli for example.


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