# The Grothendieck fundamental groups: a basic introduction

ARGOMENTI: Convegni

SEMINARIO DOTTORATO
Wednesday 15 October 2008 h. 15:00, room 1C/150

Nicola MAZZARI (Ph.D. in Pure Math., Dip. Mat. "F. Enriques", Milano)
"The Grothendieck fundamental groups: a basic introduction"

-Abstract
We give a basic introduction to the Grothendieck fundamental group. In topology there are (at least) two ways to define the fundamental group $pi_1(S,s)$ of a topological space S. Namely we can view it as
the set of loops based on a point s up to homotopy, or as the group of
automorphism of the universal cover. Only this second approach can be made algebraic and allows to define the Grothendieck (or etale) fundamental group $pi_1^et(S,s)$ of a scheme S with respect to a geometric point s. We will consider only affine schemes and we don't assume the reader familiar with algebraic geometry.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva