### 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.

Language | English (US) |
---|---|

Pages | 2017-2026 |

Number of pages | 10 |

Journal | Journal of Pure and Applied Algebra |

Volume | 214 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1 2010 |

### Fingerprint

### Keywords

- Primary
- Secondary

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Pure and Applied Algebra*,

*214*(11), 2017-2026. DOI: 10.1016/j.jpaa.2010.02.006

}

*Journal of Pure and Applied Algebra*, vol. 214, no. 11, pp. 2017-2026. DOI: 10.1016/j.jpaa.2010.02.006

**Motivic cohomology of the simplicial motive of a Rost variety.** / Merkurjev, Alexander; Suslin, Andrei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Motivic cohomology of the simplicial motive of a Rost variety

AU - Merkurjev,Alexander

AU - Suslin,Andrei

PY - 2010/11/1

Y1 - 2010/11/1

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.

KW - Primary

KW - Secondary

UR - http://www.scopus.com/inward/record.url?scp=77952891942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952891942&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2010.02.006

DO - 10.1016/j.jpaa.2010.02.006

M3 - Article

VL - 214

SP - 2017

EP - 2026

JO - Journal of Pure and Applied Algebra

T2 - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 11

ER -