Explicit descent over X(3) and X(5)

Catherine H. O'Neil

Explicit descent over X(3) and X(5)

数论 2007-05-23 v1

作者: Catherine H. O'Neil

摘要

We split the program of explicit descent of elliptic curves into two parts. For $n=3$ and $n=5,$ we first display a model for the universal elliptic curve $E$ with full level $n$ structure and describe the map of rational points of $E$ to the cohomology group $H^1(G, E[n]).$ Second, we find models in $\PP^{n-1}$ of principal homogeneous spaces of $E$ corresponding to all possible elements of $H^1(G, E[n]),$ i.e. for those elements with trivial period-index obstruction. For this we use the relationship established in \cite{me2} between the period-index obstruction and the norm symbol, a generalization of the Hilbert symbol.

关键词

elliptic curves hilbert scheme isogeny of elliptic curves

引用

@article{arxiv.math/0201321,
  title  = {Explicit descent over X(3) and X(5)},
  author = {Catherine H. O'Neil},
  journal= {arXiv preprint arXiv:math/0201321},
  year   = {2007}
}

Explicit descent over X(3) and X(5)

摘要

关键词

引用

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