The elliptic sieve and Brauer groups
| Autor: | Bhakta, Subham, Loughran, Daniel, Myerson, Simon L. Rydin, Nakahara, Masahiro |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A theorem of Serre states that almost all plane conics over $\mathbb{Q}$ have no rational point. We prove an analogue of this for families of conics parametrised by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves. We also give more general results for specialisations of Brauer groups, which yields applications to norm form equations. Comment: 32 pages |
| Databáze: | arXiv |
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