2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63591Let U be an open subset of a unirational variety (or more generally of a separably rationally connected variety). We prove that there is rational curve C in U such that the fundamental group of C surjects onto the fundamental group of U. The proof improves the earlier proof (math.AG/0003138) and works in any characteristic. Much improved version, thanks to comments of Colliot-Thélène.Algebraic Geometry14J40, 14H30text