A Note on the Growth of Sha in Dihedral Extensions

Autor:	Bell, Jamie
Rok vydání:	2024
Předmět:	Mathematics - Number Theory 11G05 (Primary) 11G40 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We provide a formula for the order of the Tate--Shafarevich group of elliptic curves over dihedral extensions of number fields of order $2n$, up to $4^{th}$ powers and primes dividing $n$. Specifically, for odd $n$ it is equal to the order of the Tate--Shafarevich group over the quadratic subextension. A similar formula holds for even $n$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.15663 Zobrazit plný text záznamu View this record from Arxiv