A Note on the Growth of Sha in Dihedral Extensions
Number Theory
2024-11-26 v1
Abstract
We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order , up to powers and primes dividing . Specifically, for odd it is equal to the order of the Tate--Shafarevich group over the quadratic subextension. A similar formula holds for even .
Cite
@article{arxiv.2411.15663,
title = {A Note on the Growth of Sha in Dihedral Extensions},
author = {Jamie Bell},
journal= {arXiv preprint arXiv:2411.15663},
year = {2024}
}