Abstract
AbstractWe give a complete answer to the local–global divisibility problem for algebraic tori. In particular, we prove that given an odd prime , if is an algebraic torus of dimension defined over a number field , then the local–global divisibility by any power holds for . We also show that this bound on the dimension is best possible, by providing a counterexample for every dimension . Finally, we prove that under certain hypotheses on the number field generated by the coordinates of the ‐torsion points of , the local–global divisibility still holds for tori of dimension less than .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.