étale

形容词 adj.
中文释义

英文释义

形容词 adj.
  1. Such that the natural homomorphism is an isomorphism. not-comparable
    — Recall (Hartshorne [1977]) that a morphism ψ: U → V is called étale if it is étale at each point u ∈ U , where being étale at u means that the natural homomorphism of local ring completions ψ*: Ô_(ψ(u)) (V) → Ôᵤ(U) is an isomorphism.

词形变化

etale alternative

词源

First applied in a mathematical context (in French) by Alexander Grothendieck to étale morphisms, apparently with reference to the phrase mer étale ("the sea at high or low tide"), the connection being that étale morphisms are, in an intuitive sense, calmly behaved or "spread out."
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