2010/11/05 by Andreas-Stephan Elsenhans, Elsenhans, Andreas-Stephan, Jörg Jahnel +1
Mathematics · #11G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11D25 #Secondary 11D85 #math.AG #math.NT #msc:11D25 #msc:11D85 #msc:11G35
paper · pdf · doi:10.48550/arxiv.1011.1430
arxiv created 2010/11/05 · arxiv updated 2010/11/08
We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over \bbQ such that \Br(S)/\Br(\bbQ) is of order two or four. This covers the vast majority of the cases when this group is non-zero. Our approach is to associate a Brauer class with every Galois invariant double-six. We show that all order two Brauer classes may be obtained in this way. We also recover Sir Peter Swinnerton-Dyer's result that \Br(S)/\Br(\bbQ) may take only five values.