Failures of weak approximation in families

2016/04/26 by M. J. Bright, T. D. Browning, D. Loughran · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Tensor decomposition and applications

paper · pdf · doi:10.1112/s0010437x16007405

Abstract

Given a family of varieties X→ ℙⁿ 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.

Cited by

• Evaluating the tame Brauer group of open varieties over local fields
• Geometric sieve over number fields for higher moments. [europepmc]

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• Non-invariance of weak approximation properties under extension of the ground field
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• Strong approximation for a family of norm varieties