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The Hasse Principle for Lines on Diagonal Surfaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Loughran, Daniel |
| Copyright Year | 2018 |
| 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 P 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://export.arxiv.org/pdf/1503.05021 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |