The elliptic sieve and Brauer groups

Subham Bhakta, Daniel Loughran, Simon Rydin Myerson, Masahiro Nakahara

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A theorem of Serre states that almost all plane conics over (Formula presented.) 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.

Original languageEnglish
Pages (from-to)1884-1922
Number of pages39
JournalProceedings of the London Mathematical Society
Issue number6
Early online date11 May 2023
Publication statusPublished - 30 Jun 2023


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