We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
AbstractCounterexamples to the Hasse Principle are constructed for curves of genus 2 to 7. These hav...
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 discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
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 an explicit model of the Jacobian variety, and give a set of quadratic defining equations...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
AbstractCounterexamples to the Hasse Principle are constructed for curves of genus 2 to 7. These hav...
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 discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
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 an explicit model of the Jacobian variety, and give a set of quadratic defining equations...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
AbstractWe describe a family of curves C of genus 2 with a maximal isotropic (Z/5)2 in J[5], where J...
Submitted to the proceedings of AGCT 12International audienceWe construct three-dimensional families...
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