The d-primary Brauer–Manin obstruction for curves

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in Number Theory Springer Journals

The d-primary Brauer–Manin obstruction for curves

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Publisher
Springer Journals
Copyright
Copyright © 2018 by SpringerNature
Subject
Mathematics; Number Theory
eISSN
2363-9555
D.O.I.
10.1007/s40993-018-0120-3
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Research in Number TheorySpringer Journals

Published: May 29, 2018

References

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