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Hélène Esnault: Finite presentation of the tame fundamental group

Time: Wed 2021-05-05 13.15

Location: Zoom, meeting ID: 685 0671 8075

Lecturer: Hélène Esnault

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.

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Belongs to: Department of Mathematics
Last changed: May 05, 2021