The d-primary Brauer–Manin obstruction for curves

For a curve over a global field we consider for which integers d the d -primary part of the Brauer group can obstruct the existence of rational points. We give examples showing it is possible that there is a d -primary obstruction for infinitely many pairwise coprime d , and also an example where th...

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Bibliographic Details
Published in:Research in number theory 2018-06, Vol.4 (2), p.1-16, Article 26
Main Authors: Creutz, Brendan, Viray, Bianca, Voloch, José Felipe
Format: Article
Language:English
Subjects:
Alliances
Integers
Mathematics
Mathematics and Statistics
Number Theory
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Summary:For a curve over a global field we consider for which integers d the d -primary part of the Brauer group can obstruct the existence of rational points. We give examples showing it is possible that there is a d -primary obstruction for infinitely many pairwise coprime d , and also an example where the odd part of the Brauer group does not obstruct although there is a Brauer–Manin obstruction. These examples demonstrate that a slightly stronger form of a conjecture of Poonen is false, despite being supported by the same heuristic.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-018-0120-3