Vol. 12, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
On a conjecture of Kato and Kuzumaki

Diego Izquierdo

Vol. 12 (2018), No. 2, 429–454
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.

Keywords
Cohomological dimension of fields, $C_i$ property, Milnor K-theory, Number fields, Function fields
Mathematical Subject Classification 2010
Primary: 11E76
Secondary: 12E25, 12E30, 14G27, 19D45, 19F99
Milestones
Received: 8 June 2017
Revised: 23 October 2017
Accepted: 18 December 2017
Published: 13 May 2018
Authors
Diego Izquierdo
Département de Mathématiques et Applications
École Normale Supérieure - CNRS, PSL Research University
Paris
France