Motivic cohomology of the simplicial motive of a Rost variety

Motivic cohomology of the simplicial motive of a Rost variety

We compute the motivic cohomology groups of the simplicial motive X θ of a Rost variety for an n -symbol θ in Galois cohomology of a field. As an application we compute the kernel and cokernel of multiplication by θ in Galois cohomology. We also show that the reduced norm map on K 2 of a division al...

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Bibliographic Details
Published in:Journal of pure and applied algebra Vol. 214; no. 11; pp. 2017 - 2026
Main Authors: Merkurjev, Alexander, Suslin, Andrei
Format: Journal Article
Language:English
Published: Elsevier B.V 01-11-2010
Subjects:
Secondary
Primary
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Summary:We compute the motivic cohomology groups of the simplicial motive X θ of a Rost variety for an n -symbol θ in Galois cohomology of a field. As an application we compute the kernel and cokernel of multiplication by θ in Galois cohomology. We also show that the reduced norm map on K 2 of a division algebra of square-free degree is injective.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2010.02.006