The Hasse principle for lines on diagonal surfaces

Research output: Research - peer-reviewArticle

  • Authors:
  • Jörg Jahnel
  • Daniel Loughran


Given a number field k and a positive integer d, in this paper we consider the following question: does there exist a smooth diagonal surface of degree d in 3 over k which contains a line over every completion of k, yet no line over k? We answer the problem using Galois cohomology, and count the number of counter-examples using a result of ErdÅs.

Bibliographical metadata

Original languageEnglish
Pages (from-to)107-119
Number of pages13
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
StatePublished - 1 Jan 2016