Norm varieties

Andrei Suslin; Seva Joukhovitski

doi:10.1016/j.jpaa.2005.12.012

Norm varieties

Andrei Suslin^*, Seva Joukhovitski

^*Corresponding author for this work

Mathematics

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

59 Scopus citations

Abstract

For given symbol in the nth Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is l-generic, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l², and a certain motivic cohomology group of this variety consists of units. The existence of such varieties is needed in Voevodsky's part of the proof of the Bloch-Kato conjecture. In the course of the proof we also establish Markus Rost's degree formula.

Original language	English (US)
Pages (from-to)	245-276
Number of pages	32
Journal	Journal of Pure and Applied Algebra
Volume	206
Issue number	1-2 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.jpaa.2005.12.012
State	Published - Jul 2006

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2005.12.012

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title = "Norm varieties",

abstract = "For given symbol in the nth Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is l-generic, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l2, and a certain motivic cohomology group of this variety consists of units. The existence of such varieties is needed in Voevodsky's part of the proof of the Bloch-Kato conjecture. In the course of the proof we also establish Markus Rost's degree formula.",

author = "Andrei Suslin and Seva Joukhovitski",

note = "Funding Information: This article is based on a series of lectures given by the first author during the fall term of 2004 at the Institute for Advanced Study. We would like to thank the following people and organizations: the Institute for providing a perfect environment for our work, the National Science Foundation for its support, Chuck Weibel for the editorial assistance, and the referee for through review and useful suggestions. ",

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doi = "10.1016/j.jpaa.2005.12.012",

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AU - Suslin, Andrei

AU - Joukhovitski, Seva

N1 - Funding Information: This article is based on a series of lectures given by the first author during the fall term of 2004 at the Institute for Advanced Study. We would like to thank the following people and organizations: the Institute for providing a perfect environment for our work, the National Science Foundation for its support, Chuck Weibel for the editorial assistance, and the referee for through review and useful suggestions.

PY - 2006/7

Y1 - 2006/7

N2 - For given symbol in the nth Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is l-generic, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l2, and a certain motivic cohomology group of this variety consists of units. The existence of such varieties is needed in Voevodsky's part of the proof of the Bloch-Kato conjecture. In the course of the proof we also establish Markus Rost's degree formula.

AB - For given symbol in the nth Milnor K-group modulo prime l we construct a splitting variety with several properties. This variety is l-generic, meaning that it is generic with respect to splitting fields having no finite extensions of degree prime to l. The degree of its top Milnor class is not divisible by l2, and a certain motivic cohomology group of this variety consists of units. The existence of such varieties is needed in Voevodsky's part of the proof of the Bloch-Kato conjecture. In the course of the proof we also establish Markus Rost's degree formula.

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DO - 10.1016/j.jpaa.2005.12.012

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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ER -

Norm varieties

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