Descent via (3,3)-isogeny on Jacobians of genus 2 curves

Nils Bruin, E. Victor Flynn, and Damiano Testa. "Descent via (3,3)-isogeny on Jacobians of genus 2 curves." Acta Arithmetica 165.3 (2014): 201-223. <http://eudml.org/doc/279018>.

@article{NilsBruin2014,
abstract = {We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/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 is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.},
author = {Nils Bruin, E. Victor Flynn, Damiano Testa},
journal = {Acta Arithmetica},
keywords = {Jacobians; Shafarevich-Tate group; class groups; isogenies; Kummer surfaces; genus 2 curves},
language = {eng},
number = {3},
pages = {201-223},
title = {Descent via (3,3)-isogeny on Jacobians of genus 2 curves},
url = {http://eudml.org/doc/279018},
volume = {165},
year = {2014},
}

TY - JOUR
AU - Nils Bruin
AU - E. Victor Flynn
AU - Damiano Testa
TI - Descent via (3,3)-isogeny on Jacobians of genus 2 curves
JO - Acta Arithmetica
PY - 2014
VL - 165
IS - 3
SP - 201
EP - 223
AB - We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/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 is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.
LA - eng
KW - Jacobians; Shafarevich-Tate group; class groups; isogenies; Kummer surfaces; genus 2 curves
UR - http://eudml.org/doc/279018
ER -