étale
Word Rarity
Very rare
Frequency: Zipf frequency 0.00 in modern English
4
Scrabble Score
5
Letters
1
Syllables
5
Unique Chars
Meaning
adj
Such that the natural homomorphism is an isomorphism.
Example Sentences
- "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."
- "Because every Deligne-Mumford stack admits an étale cover π : U → 𝔛 by a scheme, to give a sheaf of sets F on the étale site of 𝔛 is equivalent to giving a sheaf F_U together with an isomorphism between the two pull-backs of F_U to U ×_𝔛 U satisfying the cocycle condition of [26] 12.2.1."
- "We will be interested in étale maps between stacks and étale covers of stacks."
- "For a scheme X, let Ét(X) be the category of all étale morphisms from a scheme to X. An étale presheaf on X is a contravariant functor from Ét(X) to the category of sets."
Etymology
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."