Time: 9h00, Thursday, July 30, 2020

Location: Room 507-508, Building A6, Institute of Mathematics.

Abstract: In algebraic geometry, an étale morphism is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology.  In this talk, we introduce basis notions and content concerning etale morphism.