## 111.3 Books and online notes

• Laumon, Moret-Bailly: Champs Algébriques [LM-B]

This book is currently the most exhaustive reference on stacks containing many foundational results. It assumes the reader is familiar with algebraic spaces and frequently references Knutson's book [Kn]. There is an error in chapter 12 concerning the functoriality of the lisse-étale site of an algebraic stack. One doesn't need to worry about this as the error has been patched by Martin Olsson (see ) and the results in the remaining chapters (after perhaps slight modification) are correct.
• The Stacks Project Authors: Stacks Project .

• Anton Geraschenko: Lecture notes for Martin Olsson's class on stacks

This course systematically develops the theory of algebraic spaces before introducing algebraic stacks (first defined in Lecture 27!). In addition to basic properties, the course covers the equivalence between being Deligne-Mumford and having unramified diagonal, the lisse-étale site on an Artin stack, the theory of quasi-coherent sheaves, the Keel-Mori theorem, cohomological descent, and gerbes (and their relation to the Brauer group). There are also some exercises.
• Behrend, Conrad, Edidin, Fantechi, Fulton, Göttsche, and Kresch: Algebraic stacks, online notes for a book being currently written

The aim of this book is to give a friendly introduction to stacks without assuming a sophisticated background with a focus on examples and applications. Unlike [LM-B], it is not assumed that the reader has digested the theory of algebraic spaces. Instead, Deligne-Mumford stacks are introduced with algebraic spaces being a special case with part of the goal being to develop enough theory to prove the assertions in [DM]. The general theory of Artin stacks is to be developed in the second part. Only a fraction of the book is now available on Kresch's website.
• Olsson, Martin: Algebraic spaces and stacks,

Highly recommended introduction to algebraic spaces and algebraic stacks starting at the level of somebody who has mastered Hartshorne's book on algebraic geometry.

Comment #3435 by Herman Rohrbach on

Martin Olsson's book Algebraic spaces and stacks has been published a while ago: https://bookstore.ams.org/coll-62/

It probably deserves a place in this list, perhaps even replacing the lecture notes for his class (I believe his book grew out of those lecture notes).

Comment #3492 by on

Yes, of course. It is impossible to keep lists up to date; the only solution seems to be to not have lists of things. For this kind of thing, I strongly encourse people to just edit the latex file and email me. In this case I minimally added this here. Thanks.

Comment #7113 by Rakesh Pawar on

Hi, is there an active link for "Behrend, Conrad, Edidin, Fantechi, Fulton, Göttsche, and Kresch: Algebraic stacks, online notes"? Unfortunately I couldn't find it even after much of googling. Would like to see the content in this much talked about notes. :-) Thanks.

Comment #7280 by on

Not as far as I know. Maybe we should remove it?

Comment #7365 by on

The page has been archived by the Wayback Machine. At least some parts of the book are still available through it: https://web.archive.org/web/20110707004531/http://www.math.uzh.ch/index.php?pr_vo_det&key1=1287&key2=580&no_cache=1

Comment #7395 by on

@#7365. OK, I hope that people enjoy a trip into the past! Of course, one cannot cite things that once existed in a scholarly work, so maybe we should still remove this discussion from the list of books?

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