nLab Quasi-Coherent Sheaves and Tannaka Duality Theorems

This page provides links related to

• Jacob Lurie, Quasi-Coherent Sheaves and Tannaka Duality Theorems

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On quasi-coherent sheaves and Tannaka duality for geometric stacks in the context of derived algebraic geometry over E-infinity rings – E-∞ geometry

1. Generalities on spectral Deligne-Mumford stacks

1.4 Quasi-compactness of Spectral Deligne-Mumford stacks

Example

cor. 1.4.3

A spectral scheme or spectral Deligne-Mumford stack, regarded as a structured (∞,1)-topos is locally coherent.

2. Quasi-coherent sheaves

2.1 Sheaves on a spectrally ringed $\infty$-topos

2.2 Module geometries

• tangent (∞,1)-category

• geometry (for structured (∞,1)-toposes)

2.3 Quasi-coherent sheaves

• quasi-coherent sheaf

2.4 Quasi-affine spectral Deligne-Mumford stacks

2.5 Pullbacks and pushforwards of quasi-coherent sheaves

• scallop decomposition

• Grothendieck contextsix operations

2.6 Local properties of quasi-coherent sheaves

• coherent sheaf

2.7 Quasi-coherent sheaves on a functor

3. Geometric stacks and Tannaka duality

4. Coaffine stacks

5. Tannaka duality for generalized algebraic gerbes

category: reference