84 Simplicial Spaces
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Section 84.1: Introduction
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Section 84.2: Simplicial topological spaces
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Section 84.3: Simplicial sites and topoi
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Section 84.4: Augmentations of simplicial sites
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Section 84.5: Morphisms of simplicial sites
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Section 84.6: Ringed simplicial sites
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Section 84.7: Morphisms of ringed simplicial sites
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Section 84.8: Cohomology on simplicial sites
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Section 84.9: Cohomology and augmentations of simplicial sites
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Section 84.10: Cohomology on ringed simplicial sites
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Section 84.11: Cohomology and augmentations of ringed simplicial sites
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Section 84.12: Cartesian sheaves and modules
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Section 84.13: Simplicial systems of the derived category
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Section 84.14: Simplicial systems of the derived category: modules
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Section 84.15: The site associated to a semi-representable object
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Section 84.16: The site associate to a simplicial semi-representable object
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Section 84.17: Cohomological descent for hypercoverings
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Section 84.18: Cohomological descent for hypercoverings: modules
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Section 84.19: Cohomological descent for hypercoverings of an object
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Section 84.20: Cohomological descent for hypercoverings of an object: modules
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Section 84.21: Hypercovering by a simplicial object of the site
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Section 84.22: Hypercovering by a simplicial object of the site: modules
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Section 84.23: Unbounded cohomological descent for hypercoverings
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Section 84.24: Glueing complexes
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Section 84.25: Proper hypercoverings in topology
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Section 84.26: Simplicial schemes
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Section 84.27: Descent in terms of simplicial schemes
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Section 84.28: Quasi-coherent modules on simplicial schemes
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Section 84.29: Groupoids and simplicial schemes
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Section 84.30: Descent data give equivalence relations
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Section 84.31: An example case
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Section 84.32: Simplicial algebraic spaces
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Section 84.33: Fppf hypercoverings of algebraic spaces
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Section 84.34: Fppf hypercoverings of algebraic spaces: modules
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Section 84.35: Fppf descent of complexes
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Section 84.36: Proper hypercoverings of algebraic spaces