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surfaces de del pezzo

Journal of the Institute of Mathematics of Jussieu (1)

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SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN
Jean-Louis Colliot-Thélène, David A. Madore
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 3 / Issue 1 / January 2004

Published online by Cambridge University Press:

27 January 2004, pp. 1-16

Print publication:

January 2004
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Pour chaque entier $d=2,3,4$, il existe un corps $F$ de dimension cohomologique $1$ et une surface de del Pezzo de degré $d$ sur $F$ sans zéro-cycle de degré $1$, en particulier sans point rationnel. Les démonstrations utilisent le théorème de Merkur’ev et Suslin, le théorème de Riemann-Roch sur une surface et la formule du degré de Rost.