nLab proper topology

Let $S$ be a scheme. The proper topology is a Grothendieck topology on the full subcategory of proper morphisms in $Sch/S$ (the category of schemes over $S$). Namely, it is the topology generated by the pretopology where covering families are single-element families $\{ p : Y \to X \}$ with $p$ proper and surjective.

See also

• etale topology

References

• Shun-Ichi Kimura?, A cohomological characterization of Alexander schemes. Invent. math 137, 575-611 (1999).