On Tate-Shafarevich groups of abelian varieties

Details On Tate-Shafarevich groups of abelian varieties On Tate-Shafarevich groups of abelian varieties

1998-04-26

arxiv.org/abs/math/9804163v1

Mathematics

Number Theory

Scientific paper

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 ${\cyr W}(A_{^{/ F}}^{\chi})$ when $K/F$ is a quadratic extension and $A^{\chi}$ is the twist of $A$ by the non-trivial character $\chi$ of $G$.

Affiliated with

Also associated with

No associations

Rating

On Tate-Shafarevich groups of abelian varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Tate-Shafarevich groups of abelian varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Tate-Shafarevich groups of abelian varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-229374