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

Jean-Louis Colliot-Thelene·David A. Madore
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Abstract

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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Jean-Louis Colliot-Thelene, David A. Madore. 2003-05-28. Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un. https://arxiv.org/abs/math/0303168

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