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arXiv · 1503.05021

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 $\mathbb{P}^3$ 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 Erdős.

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Jörg Jahnel, Daniel Loughran. 2015-09-23. The Hasse principle for lines on diagonal surfaces. https://doi.org/10.1017/s0305004115000596

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