On a conjecture of Kato and Kuzumaki

Diego Izquierdo

doi:10.2140/ant.2018.12.429

On a conjecture of Kato and Kuzumaki

Diego Izquierdo

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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 ℂ(x₁,…, x_n) and ℂ(x₁,…, x_n)((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.

langue originale	Anglais
Pages (de - à)	429-454
Nombre de pages	26
journal	Algebra and Number Theory
Volume	12
Numéro de publication	2
Les DOIs	https://doi.org/10.2140/ant.2018.12.429
état	Publié - 1 janv. 2018

Accès au document

10.2140/ant.2018.12.429

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{af76496415bf4dd794ba3d38ab999523,

title = "On a conjecture of Kato and Kuzumaki",

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 ℂ(x1,…, xn) and ℂ(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{\textquoteright}s conjectures.",

keywords = "C property, Cohomological dimension of fields, Function fields, Milnor K-theory, Number fields",

author = "Diego Izquierdo",

year = "2018",

month = jan,

day = "1",

doi = "10.2140/ant.2018.12.429",

language = "English",

volume = "12",

pages = "429--454",

journal = "Algebra and Number Theory",

issn = "1937-0652",

number = "2",

}

TY - JOUR

T1 - On a conjecture of Kato and Kuzumaki

AU - Izquierdo, Diego

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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 ℂ(x1,…, xn) and ℂ(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.

AB - 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 ℂ(x1,…, xn) and ℂ(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.

KW - C property

KW - Cohomological dimension of fields

KW - Function fields

KW - Milnor K-theory

KW - Number fields

UR - https://www.scopus.com/pages/publications/85047237271

U2 - 10.2140/ant.2018.12.429

DO - 10.2140/ant.2018.12.429

M3 - Article

AN - SCOPUS:85047237271

SN - 1937-0652

VL - 12

SP - 429

EP - 454

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 2

ER -

On a conjecture of Kato and Kuzumaki

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Contient cette citation