Surfaces de del Pezzo sans point rationnel sur un corps de dimension cohomologique un, by Jean-Louis Colliot-Thelene and David Madore

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. (In French.)

Jean-Louis Colliot-Thelene <colliot@math.u-psud.fr>
David Madore <david.madore@ens.fr>