Motivic construction of cohomological invariants, by Nikita Semenov

The norm varieties and the varieties with special correspondences play a major role in the proof of the Bloch-Kato Conjecture by M.Rost and V.Voevodsky. In the present paper we show that a variety which possesses a special correspondence is a norm variety.

As an unexpected application we give a positive answer to a problem of J.-P.Serre about groups of type E8 over the field of rational numbers. Apart from this we include the proof of the Voevodsky conjecture about nu_n-varieties which is due to A.Vishik. This result plays an important role in our proofs.

Nikita Semenov <semenov a t>