Name
Abstract | ||
|---|---|---|
Let X (resp. Y) be a curve of genus 1 (resp. 2) over a base field k whose characteristic does not equal 2. We give criteria for the existence of a curve Z over k whose Jacobian is up to twist (2, 2, 2)-isogenous to the products of the Jacobians of X and Y. Moreover, we give algorithms to construct the curve Z once equations for X and Y are given. The first of these is based on interpolation methods involving numerical results over C that are proved to be correct over general fields a posteriori, whereas the second involves the use of hyperplane sections of the Kummer variety of Y whose desingularization is isomorphic to X. As an application, we find a twist of a Jacobian over Q that admits a rational 70-torsion point. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1090/mcom/3627 | MATHEMATICS OF COMPUTATION |
Keywords | DocType | Volume |
Gluing, Jacobians, isogenies, explicit aspects | Journal | 90 |
Issue | ISSN | Citations |
331 | 0025-5718 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hanselman Jeroen | 1 | 0 | 0.34 |
| Schiavone Sam | 2 | 0 | 0.34 |
| Jeroen Sijsling | 3 | 2 | 2.27 |