Visibility of ideal classes

Details Visibility of ideal classes Visibility of ideal classes

2008-09-30

arxiv.org/abs/0809.5209v1

Mathematics

Number Theory

21 pages

Scientific paper

Cremona, Mazur, and others have studied what they call visibility of elements of Shafarevich-Tate groups of elliptic curves. The analogue for an abelian number field $K$ is capitulation of ideal classes of $K$ in the minimal cyclotomic field containing $K$. We develop a new method to study capitulation and use it and classical methods to compute data with the hope of gaining insight into the elliptic curve case. For example, the numerical data for number fields suggests that visibility of nontrivial Shafarevich-Tate elements might be much more common for elliptic curves of positive rank than for curves of rank 0.

Affiliated with

Also associated with

No associations

Rating

Visibility of ideal classes 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 Visibility of ideal classes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Visibility of ideal classes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-252924