Failures of weak approximation in families

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

doi:10.1112/S0010437X16007405

Failures of weak approximation in families

Number Theory 2019-02-20 v2 Algebraic Geometry

Authors: M. Bright , T. D. Browning , D. Loughran

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Abstract

Given a family of varieties $X\to \mathbb{P}^n$ over a number field $k$ , 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

weak approximation Brauer-Manin obstruction families of varieties number field locally soluble fibres arithmetic geometry

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@article{arxiv.1506.01817,
  title  = {Failures of weak approximation in families},
  author = {M. Bright and T. D. Browning and D. Loughran},
  journal= {arXiv preprint arXiv:1506.01817},
  year   = {2019}
}

Comments

44 pages; there is a new application to integral points (Theorem 1.4) and Cor 1.5 recovers a well-known result concerning the Hasse principle

Failures of weak approximation in families

Abstract

Keywords

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