Principal ideals in mod- ℓ Milnor K-theory

Charles Weibel; Inna Zakharevich

doi:10.1007/s40062-017-0176-0

Principal ideals in mod- ℓ Milnor K-theory

Charles Weibel, Inna Zakharevich

School of Arts and Sciences, Mathematics

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

Abstract

Fix a symbol a̲ in the mod-ℓ Milnor K-theory of a field k, and a norm variety X for a̲. We show that the ideal generated by a̲ is the kernel of the K-theory map induced by k⊂ k(X) and give generators for the annihilator of the ideal. When ℓ= 2 , this was done by Orlov, Vishik and Voevodsky.

Original language	English (US)
Pages (from-to)	1033-1049
Number of pages	17
Journal	Journal of Homotopy and Related Structures
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s40062-017-0176-0
State	Published - Dec 1 2017

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

Milnor K-theory
Motives
Norm variety

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title = "Principal ideals in mod- ℓ Milnor K-theory",

abstract = "Fix a symbol a̲ in the mod-ℓ Milnor K-theory of a field k, and a norm variety X for a̲. We show that the ideal generated by a̲ is the kernel of the K-theory map induced by k⊂ k(X) and give generators for the annihilator of the ideal. When ℓ= 2 , this was done by Orlov, Vishik and Voevodsky.",

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author = "Charles Weibel and Inna Zakharevich",

note = "Funding Information: Weibel was supported by NSA and NSF grants, and by the IAS Fund for Math. Zakharevich was supported by an NSF MSRFP, the University of Chicago and by the IAS Fund for Math.",

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AU - Zakharevich, Inna

N1 - Funding Information: Weibel was supported by NSA and NSF grants, and by the IAS Fund for Math. Zakharevich was supported by an NSF MSRFP, the University of Chicago and by the IAS Fund for Math.

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KW - Norm variety

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