nLab Artin stack

Idea

An Artin stack is a geometric stack over the étale site: the stack quotient of a scheme whose automorphism groups are algebraic groups.

This is the general notion of algebraic stack. But often the latter term is used in a more restrictive sense to mean Deligne-Mumford stack.

Properties

• Artin representability theorem

References

The original article:

• Michael Artin, Versal deformations and algebraic stacks, Invent Math 27 (1974) 165–189 [doi:10.1007/BF01390174, eudml:142310, pdf]

Review in the general context of algebraic stacks:

• Gérard Laumon, Laurent Moret-Bailly, Champs algébriques, Ergebn. der Mathematik und ihrer Grenzgebiete 39, Springer (2000) [doi:10.1007/978-3-540-24899-6]

• Bertrand Toen, Master course on algebraic stacks

and in the broader context of derived algebraic geometry:

• Dennis Gaitsgory, Nick Rozenblyum, Section I.2.4 in: A study in derived algebraic geometry