The Mathematical Institute, University of Oxford, Eprints Archive

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

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

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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.

Item Type:Article
Subjects:H - N > Number theory
Research Groups:Number Theory Group
ID Code:802
Deposited By:E. Victor Flynn
Deposited On:01 Sep 2009 08:34
Last Modified:01 Sep 2009 08:34

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