The Brauer–Manin obstruction for nonisotrivial curves over global function fields

Creutz, Brendan; Voloch, José Felipe

doi:10.2140/ant.2026.20.109

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The Brauer–Manin obstruction for nonisotrivial curves over global function fields

Brendan Creutz and José Felipe Voloch

Appendix: Damian Rössler

Vol. 20 (2026), No. 1, 109–117

DOI: 10.2140/ant.2026.20.109

Abstract

We prove that the set of rational points on a nonisotrivial curve of genus at least $2$ over a global function field is equal to the set of adelic points cut out by the Brauer–Manin obstruction.

Keywords

Brauer–Manin obstruction, curves over function fields

Mathematical Subject Classification

Primary: 11G30, 14G05, 14G12, 14G17

Milestones

Received: 7 September 2023

Revised: 22 December 2024

Accepted: 20 January 2025

Published: 28 November 2025

Authors

Brendan Creutz
School of Mathematics and Statistics University of Canterbury Christchurch 8140 New Zealand

José Felipe Voloch
School of Mathematics and Statistics University of Canterbury Private Bag 4800 Christchurch 8140 New Zealand

Damian Rössler
Mathematical Institute University of Oxford Andrew Wiles building Woodstock Road Oxford OX2 6GG United Kingdom

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Vol. 20, No. 1, 2026