# Lukas Horosiewicz: Fundamental groups of schemes

**Time: **
Tue 2022-02-08 10.00 - 11.00

**Location: **
Zoom

**Video link: **
623 0420 7142, contact arias@math.su.se to get the password

**Respondent: **
Lukas Horosiewicz

**Abstract:** The fundamental group of a topological space is the group of based homotopy classes at a point. The Zariski topology for schemes is not fine enough and lacks several desirable properties to construct such a group. Under suitable conditions the group of cover automorphisms of a universal covering is isomorphic to the topological fundamental group. Grothendieck introduced the étale topology and used finite étale covers to define an algebraic fundamental group of a scheme in [SGA71]. The goal of this thesis is to give an introduction to the étale fundamental group of schemes without going through Grothendieck’s more general construction of Galois categories.