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Let be a group of type over such that is a compact Lie group, let be a field of characteristic 0, and
a 5-fold Pfister form. J.-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that is split if and only if is hyperbolic?
In the present article we construct a cohomological invariant of degree 5 for groups of type with trivial Rost invariant over any field of characteristic 0, and putting 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.
Cite this article
Nikita Semenov, Motivic construction of cohomological invariants. Comment. Math. Helv. 91 (2016), no. 1, pp. 163–202