Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un

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dc.creatorColliot-Thelene, Jean-Louis
dc.creatorMadore, David A.
dc.date2003-03-13
dc.date2003-05-28
dc.date.accessioned2026-07-07T04:56:01Z
dc.date.available2026-07-07T04:56:01Z
dc.descriptionFor 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.
dc.description21 pages, in French; to appear in the Journal de l'Institut Mathematique de Jussieu; second version adds a new section refining earlier results
dc.identifierhttps://arxiv.org/abs/math/0303168
dc.identifierhttp://arxiv.org/abs/math/0303168
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66783
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject14G05, 12G10, 14C35 (Primary) 14J26, 11E76, 11D09 (Secondary)
dc.titleSurfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un
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