The Hasse principle for lines on diagonal surfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Jörg Jahnel
  • Daniel Loughran

Research Organisations

External Research Organisations

  • University of Siegen
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Details

Original languageEnglish
Pages (from-to)107-119
Number of pages13
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume160
Issue number1
Publication statusPublished - 1 Jan 2016

Abstract

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.

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Cite this

The Hasse principle for lines on diagonal surfaces. / Jahnel, Jörg; Loughran, Daniel.
In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 160, No. 1, 01.01.2016, p. 107-119.

Research output: Contribution to journal › Article › Research › peer review

Jahnel J, Loughran D. The Hasse principle for lines on diagonal surfaces. Mathematical Proceedings of the Cambridge Philosophical Society. 2016 Jan 1;160(1):107-119. doi: 10.1017/S0305004115000596
Jahnel, Jörg ; Loughran, Daniel. / The Hasse principle for lines on diagonal surfaces. In: Mathematical Proceedings of the Cambridge Philosophical Society. 2016 ; Vol. 160, No. 1. pp. 107-119.
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