Scuola Normale Superiore, Pisa, Aula Mancini.<\/p>\n
This is a report on joint work with H. Esnault and M. Schusterman.<\/span><\/span> Further information is available on the event page<\/a> on the Indico platform.<\/p>\n","protected":false},"excerpt":{"rendered":" This is a report on joint work with H. Esnault and M. Schusterman.Recall that the \u00e9tale fundamental group of a variety over an algebraically closed field of characteristic 0 is known to be a finitely presented profinite group; this is proved by…<\/p>\n
Recall that the \u00e9tale fundamental group of a variety over an algebraically closed field of characteristic 0 is known to be a finitely presented profinite group; this is proved by first reducing to varieties over the complex numbers, and then comparing with the topological fundamental group. In positive characteristics, even if we restrict to smooth varieties, finite generation fails in general for \u00e9tale fundamental groups of non-proper varieties (eg, for the affine line).<\/span><\/span>
For a smooth variety with a smooth, projective compactification with an SNC boundary divisor, we show that the tame fundamental group is a finitely presented profinite group. In particular, this holds for the \u00e9tale fundamental groups of smooth projective varieties.<\/span><\/span><\/p>\n