étaleの英語

別の表記

• etale

形容詞

étale (not comparable)

1. (mathematics) Such that the natural homomorphism is an isomorphism.
   • 1994, Aleksei Parshin, Igor Shafarevich, Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory, page 278:

     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) → Ô_u(U) is an isomorphism.

   • 2009, Rob de Jeu, James Dominic Lewis, Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch, page 96:

     Because every Deligne-Mumford stack admits an étale cover π : U → �� by a scheme, to give a sheaf of sets F on the étale site of �� is equivalent to giving a sheaf F_U together with an isomorphism between the two pull-backs of F_U to U ×_�� U satisfying the cocycle condition of [26] 12.2.1.

   • 2014, Christopher Douglas, John Francis, André Henriques, Michael Hill, Topological Modular Forms, page 53:

     We will be interested in étale maps between stacks and étale covers of stacks.

   • 2016, Thierry Vialar, Handbook of Mathematics, page 825:

     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.