Universal homeomorphism

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In algebraic geometry, a universal homeomorphism is a morphism of schemes such that, for each morphism , the base change is a homeomorphism of topological spaces.

A morphism of schemes is a universal homeomorphism if and only if it is integral, radicial and surjective.[1] 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.

References[]

  1. ^ EGA IV4, 18.12.11.
  • Grothendieck, Alexandre; Dieudonné, Jean (1967). "Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie". Publications Mathématiques de l'IHÉS. 32. doi:10.1007/bf02732123. MR 0238860.

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