A comparison between obstructions to local-global principles over semiglobal fields

David Harbater, Julia Hartmann, Valentijn Karemaker, Florian Pop

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the valuation theory of the function field, or from the geometry of a regular model of the function field. Our results compare the corresponding obstructions, proving in particular that a local-global principle with respect to valuations implies a local-global principle with respect to a sufficiently fine regular model.
Original languageEnglish
Title of host publicationAbelian Varieties and Number Theory
EditorsMoshe Jarden, Tony Shaska
PublisherAmerican Mathematical Society
Pages135-146
Number of pages12
ISBN (Electronic)978-1-4704-6423-3
ISBN (Print)978-1-4704-5207-0
DOIs
Publication statusPublished - 2021

Publication series

NameContemporary Mathematics
Volume767
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • math.NT
  • math.AG
  • 13F30, 14G05, 14H25 (primary), 14G27, 11E72 (secondary)

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