The Hasse principle for lines on diagonal surfaces

Jörg Jahnel; Daniel Loughran

doi:10.1017/S0305004115000596

The Hasse principle for lines on diagonal surfaces

Jörg Jahnel, Daniel Loughran

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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.

Original language	English
Pages (from-to)	107-119
Number of pages	13
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	160
Issue number	1
DOIs	https://doi.org/10.1017/S0305004115000596
Publication status	Published - 1 Jan 2016

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HP_for_diagonal submittedAccepted author manuscript, 328 KB

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The Hasse principle for lines on diagonal surfaces

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