Abelian varieties and curves in
Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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Dan Abramovich, Joe Harris (1991)
Compositio Mathematica
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Tomoyoshi Ibukiyama, Toshiyuki Katsura, Frans Oort (1986)
Compositio Mathematica
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Monnier, Jean-Philippe (2003)
Advances in Geometry
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Lomont, Chris (2002)
Experimental Mathematics
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Ron Donagi, Ron Livné (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Marc Coppens, Gerriet Martens (1991)
Compositio Mathematica
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Nils Bruin, E. Victor Flynn, Damiano Testa (2014)
Acta Arithmetica
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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.
Fabio Bardelli, Ciro Ciliberto, Alessandro Verra (1995)
Compositio Mathematica
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