finite étale coverings of X {\displaystyle X} . One can then define the étale fundamental group as an inverse limit of finite automorphism groups. Let X...
11 KB (1,679 words) - 16:57, 1 August 2024
the étale fundamental group of a field is its (absolute) Galois group. On the other hand, for smooth varieties X over the complex numbers, the étale fundamental...
53 KB (8,076 words) - 07:10, 6 August 2024
adjective étale refers to several closely related concepts: Étale morphism Formally étale morphism Étale cohomology Étale topology Étale fundamental group Étale...
510 bytes (77 words) - 18:03, 18 October 2017
spectrum of a discrete valuation ring). It is a generalisation of the étale fundamental group. Although its existence was conjectured by Alexander Grothendieck...
11 KB (1,710 words) - 13:23, 8 June 2024
_{p}} is the ring of p-adic integers. This group is important because of its relation to Galois theory, étale homotopy theory, and the ring of adeles. In...
12 KB (2,090 words) - 19:32, 23 July 2024
the étale fundamental group of the scheme and the étale cohomology of locally constant étale sheaves. Artin, Michael; Mazur, Barry (1969). Etale homotopy...
2 KB (247 words) - 06:01, 21 December 2021
étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology...
15 KB (2,496 words) - 07:33, 22 August 2024
mathematician. He specializes in arithmetic algebraic geometry (étale fundamental group, anabelian geometry and other topics). Stix studied mathematics...
3 KB (322 words) - 06:38, 12 January 2023
Langlands program (category Representation theory of Lie groups)
representations. In simple cases, it relates l-adic representations of the étale fundamental group of an algebraic curve to objects of the derived category of l-adic...
25 KB (2,867 words) - 11:41, 19 August 2024
an étale algebra over a field is a special type of algebra, one that is isomorphic to a finite product of finite separable field extensions. An étale algebra...
2 KB (350 words) - 04:24, 10 May 2024