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
In this thesis we accomplish four main results related to Jacobians of curves. Firstly, we find a la...
In this thesis we describe a family of Jacobian varieties of non-hyperelliptic genus 2g curves that ...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
Abstract. We present a new method to show that a principal homogeneous space of the Jacobian of a cu...
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...
It is known that, given a genus 2 curve C : y^2 = f(x), where f(x) is quintic and defined over a fie...
It is known that, given a genus 2 curve C : y^2 = f(x), where f(x) is quintic and defined over a fie...
It is known that, given a genus 2 curve C : y2 = f(x), where f(x) is quintic and defined over a fiel...
We give a parametrization of curves\nonbreakingspace C of genus 2 with a maximal isotropic (Z/3)2 in...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
In this thesis we accomplish four main results related to Jacobians of curves. Firstly, we find a la...
In this thesis we describe a family of Jacobian varieties of non-hyperelliptic genus 2g curves that ...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
We discuss approaches to computing in the Shafarevich-Tate group of Jacobians of higher genus curves...
Abstract. We present a new method to show that a principal homogeneous space of the Jacobian of a cu...
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...
It is known that, given a genus 2 curve C : y^2 = f(x), where f(x) is quintic and defined over a fie...
It is known that, given a genus 2 curve C : y^2 = f(x), where f(x) is quintic and defined over a fie...
It is known that, given a genus 2 curve C : y2 = f(x), where f(x) is quintic and defined over a fiel...
We give a parametrization of curves\nonbreakingspace C of genus 2 with a maximal isotropic (Z/3)2 in...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
In this thesis we accomplish four main results related to Jacobians of curves. Firstly, we find a la...
In this thesis we describe a family of Jacobian varieties of non-hyperelliptic genus 2g curves that ...
Much success in finding rational points on curves has been obtained by using Chabauty's Theorem, whi...
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