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 

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