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The Hasse principle for lines on diagonal surfaces
| Content Provider | Scilit |
|---|---|
| Author | Jahnel, Jörg Loughran, Daniel |
| Copyright Year | 2015 |
| Description | 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. |
| Related Links | https://www.repo.uni-hannover.de/bitstream/123456789/2385/1/hasse_principle_for_lines_on_diagonal_surfaces.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D9ACDB9933D65A5FD3F724888274B1A3/S0305004115000596a.pdf/div-class-title-the-hasse-principle-for-lines-on-diagonal-surfaces-div.pdf |
| Ending Page | 119 |
| Page Count | 13 |
| Starting Page | 107 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004115000596 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 1 |
| Volume Number | 160 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2016-01-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
