Norm forms for arbitrary number fields as products of linear polynomials

Tim D Browning; Lilian Matthiesen

doi:10.24033/asens.2348

Norm forms for arbitrary number fields as products of linear polynomials

Tim D Browning, Lilian Matthiesen

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation N_K (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.

Original language	English
Pages (from-to)	1383-1446
Number of pages	64
Journal	Annales Scientifiques de l'École Normale Supérieure
Volume	50
Issue number	6
Early online date	24 Nov 2017
DOIs	https://doi.org/10.24033/asens.2348
Publication status	Published - Nov 2017

Keywords

additive combinatorics
Brauer-Manin obstruction
descent
Hasse principle
norm forms
weak approximation

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10.24033/asens.2348

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abstract = "Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.",

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AU - Browning, Tim D

AU - Matthiesen, Lilian

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AB - Given a number field K/Q and a polynomial P ε Q [t], all of whose roots are Q, let X be the variety defined by the equation NK (x) = P (t). Combining additive combinatiorics with descent we show that the Brauer-Manin obstruction is the only obstruction to the Hesse principle and weak approximation on any smooth and projective model of X.

KW - additive combinatorics

KW - Brauer-Manin obstruction

KW - descent

KW - Hasse principle

KW - norm forms

KW - weak approximation

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M3 - Article (Academic Journal)

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JO - Annales Scientifiques de l'École Normale Supérieure

JF - Annales Scientifiques de l'École Normale Supérieure

IS - 6

ER -

Norm forms for arbitrary number fields as products of linear polynomials

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Keywords

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