Universal homeomorphism
In-game article clicks load inline without leaving the challenge.
In algebraic geometry, a universal homeomorphism is a morphism of schemes f : X → Y {\displaystyle f:X\to Y} such that, for each morphism Y ′ → Y {\displaystyle Y'\to Y}, the base change X × Y Y ′ → Y ′ {\displaystyle X\times _{Y}Y'\to Y'} is a homeomorphism of topological spaces.
A morphism of schemes is a universal homeomorphism if and only if it is integral, radicial and surjective. In particular, a morphism of locally of finite type is a universal homeomorphism if and only if it is finite, radicial and surjective.
For example, an absolute Frobenius morphism is a universal homeomorphism.
- Grothendieck, Alexandre; Dieudonné, Jean (1967). . Publications Mathématiques de l'IHÉS. 32. doi:. MR.