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Results tagged with tate-shafarevich-groups
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user 43108
6
votes
Accepted
Selmer and free rank of Elliptic Curves
You first statement is correct, both ranks are expected to be equal. In particular we have:
$$\mathrm{rank}\,\,\mathrm{Sel}_p(E/K)=\mathrm{rank}(E/K)+\mathrm{rank}\,\,Ш(E/K)[p^\infty]$$
So if either …
- 17.6k
18
votes
Accepted
Is the Tate-Shafarevich group of a rational elliptic curve finite?
MO is not the place to discuss the validity of preprints, but I think it is safe to say that the finitiness of the Tate-Shafarevich group for elliptic curves over $\mathbb{Q}$ is considered an open pr …
- 17.6k