The Stacks project

111.2 Classic references

  • Mumford: Picard groups of moduli problems [mumford_picard]

    Mumford never uses the term “stack” here but the concept is implicit in the paper; he computes the picard group of the moduli stack of elliptic curves.
  • Deligne, Mumford: The irreducibility of the space of curves of given genus [DM]

    This influential paper introduces “algebraic stacks” in the sense which are now universally called Deligne-Mumford stacks (stacks with representable diagonal which admit étale presentations by schemes). There are many foundational results without proof. The paper uses stacks to give two proofs of the irreducibility of the moduli space of curves of genus $g$.
  • Artin: Versal deformations and algebraic stacks [ArtinVersal]

    This paper introduces “algebraic stacks” which generalize Deligne-Mumford stacks and are now commonly referred to as Artin stacks, stacks with representable diagonal which admit smooth presentations by schemes. This paper gives deformation-theoretic criterion known as Artin's criterion which allows one to prove that a given moduli stack is an Artin stack without explicitly exhibiting a presentation.

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