Arnth-Jensen, A. and Flynn, E. V. (2009) Nontrivial Sha in the Jacobian of an Infinite Family of Curves of Genus 2. Journal de Théorie des Nombres de Bordeaux, 21 . pp. 1-13. ISSN 1246-7405
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.
|Subjects:||H - N > Number theory|
|Research Groups:||Number Theory Group|
|Deposited By:||E. Victor Flynn|
|Deposited On:||01 Sep 2009 07:34|
|Last Modified:||29 May 2015 18:29|
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