Tate Safarevich groups of elliptic curves with complex multiplication

J. Coates; Z. Liang; R. Sujatha

Tate Safarevich groups of elliptic curves with complex multiplication

Number Theory 2009-01-27 v1

Authors: J. Coates , Z. Liang , R. Sujatha

Abstract

We show that the number of copies of ${\Bbb Q}_p/{\Bbb Z}_p$ in the Tate-Shafarevich group of an elliptic curve $E$ over ${\Bbb Q}$ with complex multipication, is at most $2p - g$ , where $g$ is the rank of $E({\Bbb Q})$ , and for all sufficiently large good ordinary primes $p$ .

Keywords

elliptic curves hyperelliptic curves finite groups

Cite

@article{arxiv.0901.3832,
  title  = {Tate Safarevich groups of elliptic curves with complex multiplication},
  author = {J. Coates and Z. Liang and R. Sujatha},
  journal= {arXiv preprint arXiv:0901.3832},
  year   = {2009}
}

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