Principe local-global pour les corps de fonctions sur des corps locaux supérieurs I

Diego Izquierdo

doi:10.1016/j.jnt.2015.05.005

Principe local-global pour les corps de fonctions sur des corps locaux supérieurs I

Diego Izquierdo

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

5 Citations (Scopus)

Abstract

Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. We give examples and counter-examples to the local-global principle for central simple algebras over K, which is an important hypothesis for having Poitou-Tate exact sequences for tori over K.

Original language	French
Pages (from-to)	250-270
Number of pages	21
Journal	Journal of Number Theory
Volume	157
DOIs	https://doi.org/10.1016/j.jnt.2015.05.005
Publication status	Published - 1 Dec 2015

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10.1016/j.jnt.2015.05.005

Cite this

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title = "Principe local-global pour les corps de fonctions sur des corps locaux sup{\'e}rieurs I",

abstract = "Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. We give examples and counter-examples to the local-global principle for central simple algebras over K, which is an important hypothesis for having Poitou-Tate exact sequences for tori over K.",

keywords = "Arithmetic duality, Brauer group, Central simple algebras, Function fields, Higher-dimensional local fields, Local-global principle, Tate-Shafarevich group",

author = "Diego Izquierdo",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = dec,

day = "1",

doi = "10.1016/j.jnt.2015.05.005",

language = "Fran{\c c}ais",

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pages = "250--270",

journal = "Journal of Number Theory",

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T1 - Principe local-global pour les corps de fonctions sur des corps locaux supérieurs I

AU - Izquierdo, Diego

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. We give examples and counter-examples to the local-global principle for central simple algebras over K, which is an important hypothesis for having Poitou-Tate exact sequences for tori over K.

AB - Let K be the function field of a smooth projective curve X over a higher-dimensional local field k. We give examples and counter-examples to the local-global principle for central simple algebras over K, which is an important hypothesis for having Poitou-Tate exact sequences for tori over K.

KW - Arithmetic duality

KW - Brauer group

KW - Central simple algebras

KW - Function fields

KW - Higher-dimensional local fields

KW - Local-global principle

KW - Tate-Shafarevich group

U2 - 10.1016/j.jnt.2015.05.005

DO - 10.1016/j.jnt.2015.05.005

M3 - Article

AN - SCOPUS:84936851669

SN - 0022-314X

VL - 157

SP - 250

EP - 270

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -