SEMINARIO DI MATEMATICA

mercoledì 28 marzo 2007

ore 16.00

Scuola Normale Superiore

Pisa

(Aula Russo)

Niels Borne

Université de Lille

Terrà  un seminario dal titolo:

“An algebraic approach of fundamental

 groups of pointed curves”

Abstract

Let X be a smooth projective algebraic curve over an algebraically closed field of characteristic zero, and D a finite set of points. Then the étale fundamental group of X-D (that by definition classifies finite covers of X unramified outside of D) is well known by analytic methods : this is the (profinite) topological fundamental group of a Riemann surface of same genus. A famous problem is to find an algebraic proof of this fact. I will start with the central example where X is the projective line minus 3 points, and show that we can describe algebraically the solvable covers in this case. Then I will describe a more general attempt, based on parabolic sheaves.

Tutti gli interessati sono invitati a partecipare.