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arXiv · 2109.03746

The elliptic sieve and Brauer groups

Subham Bhakta·Daniel Loughran·Simon L. Rydin Myerson·Masahiro Nakahara
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Abstract

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.

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Subham Bhakta, Daniel Loughran, Simon L. Rydin Myerson, Masahiro Nakahara. 2021-09-08. The elliptic sieve and Brauer groups. https://arxiv.org/abs/2109.03746

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