SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN

Jean-Louis Colliot-Thélène; David A. Madore

doi:10.1017/S1474748004000015

Abstract

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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.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Fokas, A S and Its, A R 2004. The nonlinear Schrödinger equation on the interval. Journal of Physics A: Mathematical and General, Vol. 37, Issue. 23, p. 6091.

Colliot-Thélène, J.-L. 2005. Algebra and Number Theory. p. 1.

Karpenko, Nikita A. 2006. A bound for canonical dimension of the (semi)spinor groups. Duke Mathematical Journal, Vol. 133, Issue. 2,

Colliot-Thélène, Jean-Louis 2007. Fibre spéciale des hypersurfaces de petit degré. Comptes Rendus. Mathématique, Vol. 346, Issue. 1-2, p. 63.

Zainoulline, K. 2010. Degree formula for connective K-theory. Inventiones mathematicae, Vol. 179, Issue. 3, p. 507.

Colliot-Thélène, Jean-Louis 2011. Arithmetic Geometry. Vol. 2009, Issue. , p. 1.

Colliot-Thélène, Jean-Louis and Voisin, Claire 2012. Cohomologie non ramifiée et conjecture de Hodge entière. Duke Mathematical Journal, Vol. 161, Issue. 5,

Sivatski, A. S. 2014. Faddeev invariants for central simple algebras over rational function fields. Manuscripta Mathematica, Vol. 145, Issue. 1-2, p. 71.

Wittenberg, Olivier 2015. Sur une conjecture de Kato et Kuzumaki concernant les hypersurfaces de Fano. Duke Mathematical Journal, Vol. 164, Issue. 11,

Duesler, Bradley and Knecht, Amanda 2017. Rationally connected varieties over the maximally unramified extension of $p$-adic fields. Rocky Mountain Journal of Mathematics, Vol. 47, Issue. 8,

Izquierdo, Diego 2018. On a conjecture of Kato and Kuzumaki. Algebra & Number Theory, Vol. 12, Issue. 2, p. 429.

Benoist, Olivier 2019. The period-index problem for real surfaces. Publications mathématiques de l'IHÉS, Vol. 130, Issue. 1, p. 63.

Benoist, Olivier and Wittenberg, Olivier 2020. On the integral Hodge conjecture for real varieties, I. Inventiones mathematicae, Vol. 222, Issue. 1, p. 1.

Becher, Karim Johannes 2020. Biquaternion division algebras over rational function fields. Journal of Pure and Applied Algebra, Vol. 224, Issue. 7, p. 106282.

Chipchakov, Ivan D. 2022. Fields of dimension one algebraic over a global or local field need not be of type C1. Journal of Number Theory, Vol. 235, Issue. , p. 484.

Becher, Karim Johannes and Gupta, Parul 2022. Square-reflexive polynomials. Journal of Number Theory, Vol. 238, Issue. , p. 502.

Izquierdo, Diego and Lucchini Arteche, Giancarlo 2024. On Kato and Kuzumaki’s properties for the Milnor K2 of function fields of p-adic curves. Algebra & Number Theory, Vol. 18, Issue. 4, p. 815.

Daans, Nicolas 2024. Linkage of Pfister forms over semi-global fields. Mathematische Zeitschrift, Vol. 308, Issue. 3,

Rosas-Soto, Iván 2025. Étale degree map and 0-cycles. Journal of Algebra, Vol. 665, Issue. , p. 384.

Article contents

SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

SURFACES DE DEL PEZZO SANS POINT RATIONNEL SUR UN CORPS DE DIMENSION COHOMOLOGIQUE UN

Abstract

Keywords

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