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Flat topology

In mathematics, the flat topology is a Grothendieck topology used in algebraic geometry. It is used to define the theory of flat cohomology; it also plays a fundamental role in the theory of descent (faithfully flat descent). The term flat here comes from flat modules.

Flat cohomology, The big and small fppf sites & Example

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The big and small fppf sites

Flat cohomology

Example

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Flat topology

Nodes22
Edges21
Triples10
Avg. degree1.91
Density0.090909
Components1

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Flat topology

Top relations

related to Example · 8
Flat topology → For, However, Rx, Spec, Suppose, The, There, We
is a · 1
Flat topology → Grothendieck topology used in algebraic geometry

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Important terminology

flat topology fpqc fppf faithfully affine schemes covering cohomology family morphism pretopology morphisms cover open finite topologies surjective category fixed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Flat topologyis aGrothendieck topology used in algebraic geometry0.90text
quasi compactness or finite presentation is not used much as it is not subcanonicalinstance offaithfully flat topology without any further finiteness conditions0.80text
Flat topologyrelated to ExampleThe0.60section
Flat topologyrelated to ExampleSuppose0.60section
Flat topologyrelated to ExampleFor0.60section
Flat topologyrelated to ExampleRx0.60section
Flat topologyrelated to ExampleWe0.60section
Flat topologyrelated to ExampleThere0.60section
Flat topologyrelated to ExampleSpec0.60section
Flat topologyrelated to ExampleHowever0.60section

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