Article contents
The Hasse principle for lines on diagonal surfaces
Published online by Cambridge University Press: 30 October 2015
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 1 , January 2016 , pp. 107 - 119
- Copyright
- Copyright © Cambridge Philosophical Society 2015
References
REFERENCES
- 1
- Cited by