On Tate-Shafarevich groups of abelian varieties
| dc.creator | Gonzalez-Avilés, Cristian D. | |
| dc.date | 1998-04-26 | |
| dc.date.accessioned | 2026-07-07T05:24:39Z | |
| dc.date.available | 2026-07-07T05:24:39Z | |
| dc.description | Let $K/F$ be a finite Galois extension of number fields with Galois group $G$, let $A$ be an abelian variety defined over $F$, and let ${\cyr W}(A_{^{/ K}})$ and ${\cyr W}(A_{^{/ F}})$ denote, respectively, the Tate-Shafarevich groups of $A$ over $K$ and of $A$ over $F$. Assuming that these groups are finite, we derive, under certain restrictions on $A$ and $K/F$, a formula for the order of the subgroup of ${\cyr W}(A_{^{/ K}})$ of $G$-invariant elements. As a corollary, we obtain a simple formula relating the orders of ${\cyr W}(A_{^{/ K}})$, ${\cyr W}(A_{^{/ F}})$ and ${\cyr W}(A_{^{/ F}}^χ)$ when $K/F$ is a quadratic extension and $A^χ$ is the twist of $A$ by the non-trivial character $χ$ of $G$. | |
| dc.identifier | https://arxiv.org/abs/math/9804163 | |
| dc.identifier | http://arxiv.org/abs/math/9804163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76883 | |
| dc.subject | Number Theory | |
| dc.title | On Tate-Shafarevich groups of abelian varieties | |
| dc.type | text |