Nontrivial Sha in the Jacobian of an Infinite Family of Curves of Genus 2.

Author: 

Arnth-Jensen, A
Flynn, E

Publication Date: 

1 April 2009

Journal: 

J. Theor. Nombres Bordeaux

Last Updated: 

2020-05-14T03:17:49.69+01:00

Volume: 

21

page: 

1-9

abstract: 

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.

Symplectic id: 

199484

Submitted to ORA: 

Not Submitted

Publication Type: 

Conference Paper