etale morphism

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An etale morphism \(U\to X\) is:

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finite etale morphism

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Links to this page

unresolved links output

locally of finite presentation in Unsorted/Gromov-Witten invariants, -Unsorted/etale morphism, -Unsorted/formally etale

smooth morphism in Projects/2022 Algebraic Geometry Oral Exam/030 Schemes, -Unsorted/etale morphism
almost purity

Generally, purity means something happens in a particular codimension. A foundational result for perfectoid spaces. Reminiscent of Zariski–Nagata’s purity theorem: the branch locus on a nonsingular algebraic variety, the branch locus (where the morphism ramifies) is a Weil divisor, i.e. is comprised purely of codimension 1 subvarieties. This describes the locus on which a morphism can fail to be etale.