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

Artin stacks are named after Michael Artin.

See for instance

• Gérard Laumon, L. Moret-Bailly, Champs algébriques , A series of Modern

  Surveys in Mathematics vol. 39, Springer-Verlag 2000.

• Bertrand Toen, Master course on algebraic stacks.

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