List of topologies on the category of schemes

* 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
* Gabber, Ofer; Kelly, Shane (2015), "Points in algebraic geometry", J. Pure Appl. Algebra 219 (10): 4667–4680

0.00

(0 votes)

|

Retrieved from "https://handwiki.org/wiki/index.php?title=List_of_topologies_on_the_category_of_schemes&oldid=1797622"