The Stacks project

110.2 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.

Comments (0)


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Your email address will not be published.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.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 03B2. Beware of the difference between the letter 'O' and the digit '0'.