EuDML | Browse

Skip to main content (access key 's'), Skip to navigation (access key 'n'), Accessibility information (access key '0')

Subjects
11-XX Number theory
11Gxx Arithmetic algebraic geometry (Diophantine geometry)
11G10 Abelian varieties of dimension $> 1$

Items

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 2 of 2

Non-existence of points rational over number fields on Shimura curves

Keisuke Arai (2016)

Acta Arithmetica

Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.

Non-trivial $Ш$ in the Jacobian of an infinite family of curves of genus 2

Anna Arnth-Jensen, E. Victor Flynn (2009)

Journal de Théorie des Nombres de Bordeaux

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.

Currently displaying 1 – 2 of 2

Page 1

Displaying 1 – 2 of 2

Non-existence of points rational over number fields on Shimura curves

Non-trivial Ш in the Jacobian of an infinite family of curves of genus 2

Currently displaying 1 – 2 of 2

Non-trivial $Ш$ in the Jacobian of an infinite family of curves of genus 2