## 111.4 Related references on foundations of stacks

Vistoli:

*Notes on Grothendieck topologies, fibered categories and descent theory*[vistoli_fga]Contains useful facts on fibered categories, stacks and descent theory in the fpqc topology as well as rigorous proofs.

Knutson:

*Algebraic Spaces*[Kn]This book, which evolved from his PhD thesis under Michael Artin, contains the foundations of the theory of algebraic spaces. The book [LM-B] frequently references this text. See also Artin's papers on algebraic spaces: [Artin-Algebraic-Approximation], [ArtinI], [Artin-Implicit-Function], [ArtinII], [Artin-Construction-Techniques], [Artin-Algebraic-Spaces], [Artin-Theorem-Representability], and [ArtinVersal]

Grothendieck et al,

*Théorie des Topos et Cohomologie Étale des Schémas I, II, III*also known as SGA4 [SGA4]Volume 1 contains many general facts on universes, sites and fibered categories. The word “champ” (French for “stack”) appears in Deligne's Exposé XVIII.

Jean Giraud:

*Cohomologie non abélienne*[giraud]The book discusses fibered categories, stacks, torsors and gerbes over general sites but does not discuss algebraic stacks. For instance, if $G$ is a sheaf of abelian groups on $X$, then in the same way $H^1(X, G)$ can be identified with $G$-torsors, $H^2(X, G)$ can be identified with an appropriately defined set of $G$-gerbes. When $G$ is not abelian, then $H^2(X, G)$ is defined as the set of $G$-gerbes.

Kelly and Street:

*Review of the elements of 2-categories*[kelly-street]The category of stacks form a 2-category although a simple type of 2-category where are 2-morphisms are invertible. This is a reference on general 2-categories. I have never used this so I cannot say how useful it is. Also note that [stacks-project] contains some basics on 2-categories.

## Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)