The Hasse principle for lines on del Pezzo surfaces

2014/10/21 by Jörg Jahnel, Jahnel, Jörg, Daniel Loughran +1 · 1 citation
Mathematics · #11G35 (Primary) 11R32 #14-04 (Secondary) #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G35 #msc:11R32 #msc:14-04 #msc:14J26

paper · pdf · doi:10.48550/arxiv.1410.5671

32 pages

arxiv created 2015/02/25 · arxiv updated 2015/02/26

Abstract

In this paper, we consider the following problem: Does there exist a cubic surface over ℚ which contains no line over ℚ, yet contains a line over every completion of ℚ? This question may be interpreted as asking whether the Hilbert scheme of lines on a cubic surface can fail the Hasse principle. We also consider analogous problems, over arbitrary number fields, for other del Pezzo surfaces and complete intersections of two quadrics.

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• Principe local global pour les espaces linéaires sur les intersections de deux quadriques

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