nLab Representability Theorems

This page collects some links related to the article

• Jacob Lurie,

  Representability theorems

  (pdf)

of representability by Deligne-Mumford stacks in E-∞ geometry (“geometric ∞-stacks”).

This provides the main technical ingredient, Proposition 4.1, in A Survey of Elliptic Cohomology, on the Goerss-Hopkins-Miller-Lurie theorem.

More concrete implementations of the main theorem appear in

• Jonathan Pridham, Representability of derived stacks (arXiv:1011.2189)

1. Cotangent complex

• cotangent complex

2. Properties of moduli functors

2.1 Nilcomplete, Cohesive, and Integrable Functors

• cohesive ∞-presheaf on E-∞ rings

2.2 Relativized properties of functors

2.3 Finiteness conditions on functors

2.4 Moduli of spectral Deligne-Mumford stacks

• spectral Deligne-Mumford stack

3. Representability theorems

4. Tangent complexes and dualizing modules

4.1 The tangent complex

4.2 Dualizing modules

• dualizing object in a closed category

• dualizing module (Verdier duality)

4.3 Existence of dualizing modules

4.4 A linear representability criterion

4.5 Existence of cotangent complexes

category: reference