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- The most fundamental item of study in modern algebraic geometry is the category of schemes. This category admits many different Grothendieck topologies, each of which is well-suited for a different purpose. This is a list of some of the topologies on the category of schemes.
* cdh topology A variation of the h topology
* Étale topology Uses etale morphisms.
* fppf topology Faithfully flat of finite presentation
* fpqc topology Faithfully flat quasicompact
* h topology Coverings are universal topological epimorphisms
* v-topology (also called universally subtrusive topology): coverings are maps which admit liftings for extensions of valuation rings
* l′ topology A variation of the Nisnevich topology
* Nisnevich topology Uses etale morphisms, but has an extra condition about isomorphisms between residue fields.
* qfh topology Similar to the h topology with a quasifiniteness condition.
* Zariski topology Essentially equivalent to the "ordinary" Zariski topology.
* Smooth topology Uses smooth morphisms, but is usually equivalent to the etale topology (at least for schemes).
* The finest such that all representable functors are sheaves. (en)
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- 1883 (xsd:nonNegativeInteger)
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- The most fundamental item of study in modern algebraic geometry is the category of schemes. This category admits many different Grothendieck topologies, each of which is well-suited for a different purpose. This is a list of some of the topologies on the category of schemes. (en)
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- List of topologies on the category of schemes (en)
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