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2018 On a conjecture of Kato and Kuzumaki
Diego Izquierdo
Algebra Number Theory 12(2): 429-454 (2018). DOI: 10.2140/ant.2018.12.429

Abstract

In 1986, Kato and Kuzumaki stated several conjectures in order to give a diophantine characterization of cohomological dimension of fields in terms of projective hypersurfaces of small degree and Milnor K-theory. We establish these conjectures for finite extensions of (x1,,xn) and (x1,,xn)((t)), and we prove new local-global principles over number fields and global fields of positive characteristic in the context of Kato and Kuzumaki’s conjectures.

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Diego Izquierdo. "On a conjecture of Kato and Kuzumaki." Algebra Number Theory 12 (2) 429 - 454, 2018. https://doi.org/10.2140/ant.2018.12.429

Information

Received: 8 June 2017; Revised: 23 October 2017; Accepted: 18 December 2017; Published: 2018
First available in Project Euclid: 23 May 2018

zbMATH: 06880894
MathSciNet: MR3803709
Digital Object Identifier: 10.2140/ant.2018.12.429

Subjects:
Primary: 11E76
Secondary: 12E25, 12E30, 14G27, 19D45, 19F99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2018
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