Translator Disclaimer
2020 On the norm and multiplication principles for norm varieties
Shira Gilat, Eliyahu Matzri
Ann. K-Theory 5(4): 709-720 (2020). DOI: 10.2140/akt.2020.5.709

Abstract

Let p be a prime, and suppose that F is a field of characteristic zero which is p-special (that is, every finite field extension of F has dimension a power of p). Let α𝒦nM(F)p be a nonzero symbol and XF a norm variety for α. We show that X has a 𝒦mM-norm principle for any m, extending the known 𝒦1M-norm principle. As a corollary we get an improved description of the kernel of multiplication by a symbol. We also give a new proof for the norm principle for division algebras over p-special fields by proving a decomposition theorem for polynomials over F-central division algebras. Finally, for p=n=m=2 we show that the known 𝒦1M-multiplication principle cannot be extended to a 𝒦2M-multiplication principle for X.

Citation

Download Citation

Shira Gilat. Eliyahu Matzri. "On the norm and multiplication principles for norm varieties." Ann. K-Theory 5 (4) 709 - 720, 2020. https://doi.org/10.2140/akt.2020.5.709

Information

Received: 31 October 2019; Accepted: 12 August 2020; Published: 2020
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/akt.2020.5.709

Subjects:
Primary: 19D45

Keywords: Milnor $K\mkern-2mu$-theory , norm varieties , symbols

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.5 • No. 4 • 2020
MSP
Back to Top