A positive proportion of Hasse principle failures in a family of Châtelet surfaces

Nick Rome*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We investigate a family of Châtelet surfaces over Q and develop an asymptotic formula for the frequency of Hasse principle failures. We show that a positive proportion (roughly 23.7%) of such surfaces fails the Hasse principle, by building on previous work of De La Bretèche and Browning.

Original languageEnglish
Pages (from-to)1237-1249
Number of pages13
JournalInternational Journal of Number Theory
Volume15
Issue number6
Early online date13 Feb 2019
DOIs
Publication statusPublished - 1 Jul 2019

Keywords

  • Brauer-Manin obstruction
  • Châtelet surfaces
  • Hasse principle

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