Descent via (3,3)-isogeny on Jacobians of genus 2 curves
arXiv:1401.0580 · doi:10.4064/aa165-3-1
Abstract
We give parametrisation of curves C of genus 2 with a maximal isotropic (ZZ/3)^2 in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it can shown that non-reducible Jacobians have nontrivial 3-part of the Tate-Shafarevich group.
17 pages