Motivic Construction of Cohomological Invariants

@inproceedings{Semenov2015MotivicCO,
  title={Motivic Construction of Cohomological Invariants},
  author={Nikita Semenov},
  year={2015}
}
Let G be a group of type E8 over Q such that GR is a compact Lie group, let K be a field of characteristic 0, and q = 〈〈−1,−1,−1,−1,−1〉〉 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 GK is split if and only if qK is hyperbolic? 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 k = Q answer… CONTINUE READING

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