Explicit descent over X(3) and X(5)
| dc.creator | O'Neil, Catherine H. | |
| dc.date | 2002-01-16 | |
| dc.date.accessioned | 2026-07-07T04:46:14Z | |
| dc.date.available | 2026-07-07T04:46:14Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0201321 | |
| dc.identifier | http://arxiv.org/abs/math/0201321 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63251 | |
| dc.subject | Number Theory | |
| dc.title | Explicit descent over X(3) and X(5) | |
| dc.type | text |