nLab Spectral Schemes

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• Jacob Lurie,

  Spectral Schemes (pdf)

This studies the theory of generalized scheme whose structure sheaf takes values in E-∞ ring-spectra. Hence structured (∞,1)-toposes in E-∞ geometry.

See at E-∞ scheme.

See also

• Paul Goerss, Topological Algebraic Geometry - A Workshop

Sheaves of spectra

• sheaf of spectra

• stabilization via sheaves of spectra

• inclusion of sheaves of connective spectra

Spectral schemes

• E-infinity scheme

Coherent $\infty$-Topoi

• coherent (∞,1)-topos

• compact topos

• n-coherent object

Deligne’s completeness theorem

• Deligne-Lurie completeness theorem

• Deligne completeness theorem

Flat descent

Flat descent for modules

Digression: Henselian rings

Spectral Deligne-Mumford stacks

• spectral Deligne-Mumford stack

Comparison results

category: reference