nLab derived moduli space

Idea

A derived moduli stack is a moduli space in the context of derived algebraic geometry.

The existence of derived moduli stacks was first conjectured by Maxim Kontsevich, see hidden smoothness principle.

Related concepts

• classifying space, classifying stack, moduli space, moduli stack

• classifying topos

• universal principal bundle, universal principal infinity-bundle

• classifying morphism

References

The first examples of derived moduli spaces, using the language of dg-schemes, were constructed in

• Ionut Ciocan-Fontanine, Mikhail Kapranov, Derived Quot

  schemes_, 1999, arXiv:math/9905174.

• Ionut Ciocan-Fontanine, Mikhail Kapranov, Derived Hilbert

  schemes_, 2000, arXiv:math/0005155.

In the language of derived algebraic geometry they were considered in

• Jacob Lurie, Moduli Problems and DG-Lie Algebras

• J. P. Pridham, Representability of derived stacks, arxiv/1011.2189

For the construction of the derived moduli stack of perfect complexes on a smooth proper scheme, see

• Bertrand Toen, Michel Vaquie, Moduli of objects in dg-categories, 2007, arXiv:math/0503269.