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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
; | | Date: |
13 Mar 2003 | | Subject: | Number Theory; Algebraic Geometry MSC-class: 14G05, 12G10, 14C35 (Primary) 14J26, 11E76, 11D09 (Secondary) | math.NT math.AG | | 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. | | Source: | arXiv, math.NT/0303168 | | Services: | Forum | Review | PDF | Favorites | |
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