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...

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...

adjective étale refers to several closely related concepts: Étale morphism Formally étale morphism Étale cohomology Étale topology Étale fundamental group Étale...

spectrum of a discrete valuation ring). It is a generalisation of the étale fundamental group. Although its existence was conjectured by Alexander Grothendieck...

étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology...

_{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...

the étale fundamental group of the scheme and the étale cohomology of locally constant étale sheaves. Artin, Michael; Mazur, Barry (1969). Etale homotopy...

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...

mathematician. He specializes in arithmetic algebraic geometry (étale fundamental group, anabelian geometry and other topics). Stix studied mathematics...

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...