2009/05/27 by Nikita Semenov, Semenov, Nikita
Mathematics · #19E15 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:19E15 #msc:20G15
paper · pdf · doi:10.48550/arxiv.0905.4384
34 pages
arxiv created 2015/04/26 · arxiv updated 2015/04/28
Let G be a group of type E8 of compact type over the field of rational numbers, let K be a field of characteristic 0, and q the 5-fold Pfister form which is the sum of 32 squares. J-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that G is split over K if and only if q is hyperbolic over K? In the present article we construct a cohomological invariant of degree 5 for groups of type E8 with trivial Rost invariant over any field k of characteristic 0, and putting the field of rational numbers for k answer positively this question of Serre. Aside from that, we show that a variety which possesses a special correspondence of Rost is a norm variety.