EXPLICIT n-DESCENT ON ELLIPTIC CURVES II. GEOMETRY

@inproceedings{Fisher2006EXPLICITNO,
  title={EXPLICIT n-DESCENT ON ELLIPTIC CURVES II. GEOMETRY},
  author={T. A. Fisher and Catherine O’Neil and D. Simon and M. Stoll},
  year={2006}
}
This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in Pn−1. The main tool we use is a comparison between an easily obtained embedding into Pn2−1 and another map into Pn2−1 that factors through the Segre embedding Pn−1×Pn−1 → Pn2−1. The comparison relies on an explicit version of the local-to-global principle for the n-torsion of the… CONTINUE READING

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