Motivic cohomology of the simplicial motive of a Rost variety

Alexander Merkurjev; Andrei Suslin

doi:10.1016/j.jpaa.2010.02.006

Motivic cohomology of the simplicial motive of a Rost variety

Alexander Merkurjev^*, Andrei Suslin

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We compute the motivic cohomology groups of the simplicial motive Xθ 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 K2 of a division algebra of square-free degree is injective.

Original language	English (US)
Pages (from-to)	2017-2026
Number of pages	10
Journal	Journal of Pure and Applied Algebra
Volume	214
Issue number	11
DOIs	https://doi.org/10.1016/j.jpaa.2010.02.006
State	Published - Nov 2010

Funding

We are grateful to the referee for the useful comments. The first author acknowledges support by the NSF grant DMS #0652316. The second author acknowledges support by the NSF grant DMS #0901852.

Keywords

Primary
Secondary

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2010.02.006

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abstract = "We compute the motivic cohomology groups of the simplicial motive Xθ 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 K2 of a division algebra of square-free degree is injective.",

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AU - Suslin, Andrei

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N2 - We compute the motivic cohomology groups of the simplicial motive Xθ 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 K2 of a division algebra of square-free degree is injective.

AB - We compute the motivic cohomology groups of the simplicial motive Xθ 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 K2 of a division algebra of square-free degree is injective.

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ER -

Motivic cohomology of the simplicial motive of a Rost variety

Abstract

Funding

Keywords

ASJC Scopus subject areas

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