Descent via (3,3)-isogeny on Jacobians of genus 2 curves

• Autorzy: Nils Bruin , E. Victor Flynn , Damiano Testa
• Języki publikacji: EN

Abstrakty

EN

We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.

Kategorie tematyczne

• 11G10: Abelian varieties of dimension > 1
• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14H40: Jacobians, Prym varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 3
• Strony: 201-223

Daty

wydano

2014

Twórcy

autor

Nils Bruin

• Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6

autor

E. Victor Flynn

• Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom

autor

Damiano Testa

• Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom

Identyfikatory

DOI

10.4064/aa165-3-1