| 释义 |
- References
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).
- Canonical topology The finest such that all representable functors are sheaves.
References - Belmans, Pieter. Grothendieck topologies and étale cohomology
- {{citation|first1=Ofer|last1=Gabber|author1-link=Ofer Gabber|first2=Shane|last2=Kelly|arxiv=1407.5782|title=Points in algebraic geometry|journal= J. Pure Appl. Algebra|volume=219|year=2015|issue=10|pages=4667–4680}}
1 : Algebraic geometry |