Failures of weak approximation in families

M. J. Bright; T. D. Browning; D. Loughran

doi:10.1112/S0010437X16007405

Failures of weak approximation in families

M. J. Bright^*, T. D. Browning, D. Loughran

^*Corresponding author for this work

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

33 Citations (Scopus)

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Abstract

Given a family of varieties X → Ρⁿ over a number field, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for 100% of the fibres which are everywhere locally soluble.

Original language	English
Pages (from-to)	1435-1475
Number of pages	41
Journal	Compositio Mathematica
Volume	7
Issue number	152
Early online date	26 Apr 2016
DOIs	https://doi.org/10.1112/S0010437X16007405
Publication status	Published - 1 Jul 2016

Keywords

Brauer–Manin obstruction
fibrations
rational points
sieves
weak approximation

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title = "Failures of weak approximation in families",

abstract = "Given a family of varieties X → Ρn over a number field, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for 100\% of the fibres which are everywhere locally soluble.",

keywords = "Brauer–Manin obstruction, fibrations, rational points, sieves, weak approximation",

author = "Bright, \{M. J.\} and Browning, \{T. D.\} and D. Loughran",

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T1 - Failures of weak approximation in families

AU - Bright, M. J.

AU - Browning, T. D.

AU - Loughran, D.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - Given a family of varieties X → Ρn over a number field, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for 100% of the fibres which are everywhere locally soluble.

AB - Given a family of varieties X → Ρn over a number field, we determine conditions under which there is a Brauer-Manin obstruction to weak approximation for 100% of the fibres which are everywhere locally soluble.

KW - Brauer–Manin obstruction

KW - fibrations

KW - rational points

KW - sieves

KW - weak approximation

UR - https://www.scopus.com/pages/publications/84966534375

U2 - 10.1112/S0010437X16007405

DO - 10.1112/S0010437X16007405

M3 - Article (Academic Journal)

SN - 0010-437X

VL - 7

SP - 1435

EP - 1475

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 152

ER -

Failures of weak approximation in families

Abstract

Keywords

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