2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58886Let U be an open subset of a unirational 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. As a consequence we obtain new proofs of the theorems of Harbater and Colliot-Thélène on Galois covers and torsors over the p-adic line. We also obtain examples of pencils of curves of genus <14 whose monodromy group is the full Teichmüller group.12 pages, LaTeXAlgebraic Geometry14J45 (Primary) 14E20, 14F35, 14H15 (Secondary)text