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The role of primes of good reduction in the Brauer–Manin obstruction

Margherita Pagano
Vol. 20 (2026), No. 7, 1263–1300
DOI: 10.2140/ant.2026.20.1263
Abstract

We discuss the role of primes of good reduction in the existence of the Brauer–Manin obstruction to weak approximation for varieties defined over number fields. Following Bright and Newton, we give conditions on the ramification index of primes involved in the Brauer–Manin obstruction. To support the results, we give many examples of transcendental nature on K3 surfaces.

Keywords
rational points, Brauer group, Brauer–Manin obstruction
Mathematical Subject Classification
Primary: 14F22, 14G05, 14G12, 14G17, 14G20
Secondary: 14F30
Milestones
Received: 26 September 2023
Revised: 23 May 2025
Accepted: 1 July 2025
Published: 14 August 2026
Authors
Margherita Pagano
Department of Mathematics
Imperial College London
London
United Kingdom
© 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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