AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J is the Jacobian variety of C, and develop the theory required to perform descent via (5,5)-isogeny. We apply this to several examples, where it can be shown that non-reducible Jacobians have nontrivial 5-part of the Tate–Shafarevich group
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
We present a quasi-linear algorithm to compute isogenies between Jacobians of curvesof genus 2 and 3...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
We suggest that the following plan will provide a powerful tool for trying to find the set of Q-rati...
International audienceLet ell be a prime, and H a curve of genus 2 over a field k of characteristic ...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
We give a parametrization of curves\nonbreakingspace C of genus 2 with a maximal isotropic (Z/3)2 in...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
We present a quasi-linear algorithm to compute isogenies between Jacobians of curvesof genus 2 and 3...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
International audienceWe construct six infinite series of families of pairs of curves (X,Y) of arbit...
We suggest that the following plan will provide a powerful tool for trying to find the set of Q-rati...
International audienceLet ell be a prime, and H a curve of genus 2 over a field k of characteristic ...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
We give a parametrization of curves\nonbreakingspace C of genus 2 with a maximal isotropic (Z/3)2 in...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
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