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

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

2003-03-13

arxiv.org/abs/math/0303168v2

Mathematics

Number Theory

21 pages, in French; to appear in the Journal de l'Institut Mathematique de Jussieu; second version adds a new section refinin

Scientific paper

For 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.

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