## 112.2 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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