2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66783For each integer d=2,3,4, there exists a field F with cohomological dimension 1 and a del Pezzo surface of degree d over F having no rational point. Proofs use the theorem of Merkur'ev and Suslin, the Riemann-Roch theorem on a surface and Rost's degree formula. ----- Pour chaque entier d=2,3,4, il existe un corps F de dimension cohomologique 1 et une surface de del Pezzo de degre d sur F sans point rationnel. Les demonstrations utilisent le theoreme de Merkur'ev et Suslin, le theoreme de Riemann-Roch sur une surface et la formule du degre de Rost.21 pages, in French; to appear in the Journal de l'Institut Mathematique de Jussieu; second version adds a new section refining earlier resultsNumber TheoryAlgebraic Geometry14G05, 12G10, 14C35 (Primary) 14J26, 11E76, 11D09 (Secondary)text