Motivic construction of cohomological invariants

Details Motivic construction of cohomological invariants Motivic construction of cohomological invariants

2009-05-27

arxiv.org/abs/0905.4384v2

Mathematics

Algebraic Geometry

33 pages

Scientific paper

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. The proof heavily uses the motivic cohomology and the category of effective motives of Voevodsky. 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.

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