WebIn commutative algebra and algebraic geometry, a morphism is called formally étale if it has a lifting property that is analogous to being a local diffeomorphism. Wikiwand is the … WebEtale morphisms are morphisms of schemes, while etale maps are maps of rings that induce etale morphisms under the functor spec. However, obtaining an explicit characterization of such maps is not in general easy, and I believe it uses Zariski's main theorem. – Harry Gindi Dec 10, 2009 at 15:54 1
Étale - Wikipedia
WebOct 3, 2024 · Smooth (resp. étale) morphisms are just locally finitely presented + formally smooth (resp. étale) morphisms. For unramified morphisms, it is originally defined in EGA as locally finitely presented + formally unramified morphisms, but now they are widely accepted as locally of finite type + formally unramified morphisms. WebA morphism is étale if and only if it is smooth of relative dimension (see Definition 29.34.13 ). A pleasing feature of the definition is that the set of points where a morphism is étale is automatically open. Note that there is no separation or … kenyon mn weather
Unrami ed morphisms - University of California, Berkeley
Since the structure sheaf of a scheme naturally carries only the discrete topology, the notion of formally étale for schemes is analogous to formally étale for the discrete topology for rings. That is, a morphism of schemes f : X → Y is formally étale if for every affine Y-scheme Z, every nilpotent sheaf of ideals J on Z … See more In commutative algebra and algebraic geometry, a morphism is called formally étale if it has a lifting property that is analogous to being a local diffeomorphism. See more • Open immersions are formally étale. • The property of being formally étale is preserved under composites, base change, and See more • Formally unramified • Formally smooth • Étale morphism See more Let A be a topological ring, and let B be a topological A-algebra. Then B is formally étale if for all discrete A-algebras C, all nilpotent ideals J of C, and all continuous A-homomorphisms u : B → C/J, there exists a unique continuous A-algebra map v : B → C such that … See more • Localizations are formally étale. • Finite separable field extensions are formally étale. More generally, any (commutative) flat See more WebApr 6, 2024 · étale morphism of schemes, formally étale morphism of schemes. étale site, pro-étale site, étale (∞,1)-site. Deligne-Mumford stack. ℓ-adic cohomology. Contents. Idea; Definition; ... James Milne, Etale cohomology, Princeton Mathematical Series 33, 1980. xiii+323 pp. A detailed survey is in chapter 34 of. Aise Johan de Jong, ... WebDe nition 1 A morphism f:X!Y is smooth if it is locally of nite presen-tation and formally smooth. It is clear from the de nition that Iis an ideal in an R-algebra A, then the map An(A) !An(A=I) is surjective. This is in particular true if Iis nilpotent so that An!SpecRis formally smooth, hence smooth. is iran a monarchy