Hélène Esnault: Finite presentation of the tame fundamental group

Abstract

Recall that if \(X\) is smooth complex projective, its underlying complex topological space is a finite \(CW\) complex, thus its topological fundamental group is finitely presented, thus its profinite completion, that is by the Riemann existence theorem its étale fundamental group, is as a profinite group finitely presented as well. If \(X\) is a smooth variety over an algebraic closed char. \(p>0\) field, which admits a good compactification, we prove that its tame fundamental group is finitely presented as a profinite group.

Joint work with Mark Schusterman and V. Srinivas.