The elliptic sieve and Brauer groups
Number Theory
2023-03-20 v3 Algebraic Geometry
Abstract
A theorem of Serre states that almost all plane conics over 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.
Cite
@article{arxiv.2109.03746,
title = {The elliptic sieve and Brauer groups},
author = {Subham Bhakta and Daniel Loughran and Simon L. Rydin Myerson and Masahiro Nakahara},
journal= {arXiv preprint arXiv:2109.03746},
year = {2023}
}
Comments
32 pages